I I I I 74-3189
HANHAM, Robert Quentin, 1947- DIFFUSION OF INNOVATION FRCM A SUPPLY PERSPECTIVE: AN APPLICATION TO THE ARTIFICIAL INSEMINATION OF CATTLE IN SOUTHERN SWEDEN.
The Ohio State University, Ph.D., 1973 Geography
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. DIFFUSION OF INNOVATION FROM A SUPPLY PERSPECTIVE:
AN APPLICATION TO THE ARTIFICIAL INSEMINATION OF
CATTLE IN SOUTHERN SWEDEN
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
Robert Quentin Hanham, B.A., M .A.
*****
The Ohio State University
1973
Reading Committee: Approved By
Lawrence A. Brown
Edward J. Taaffe
Kevin R. Cox
Adviser Department of Geography ACKNOWLEDGEMENTS
I am very much Indebted to Professor L.A. Brown, my adviser, for suggesting the particular topic upon which this dissertation is based, and for providing the data and many useful comments and criticisms. I also wish to thank Chose members of the reading committee,
Professor E. Casetti and Professor K.R. Cox, together with John Agnew, Paul Herr, Merle Maloff, Aron Spector,
Dr. C.E. Youngmann, Dr. P.C. Watson and Richard Zeller for providing me with technical and spiritual guidance.
This is a portion of ongoing research on the diffusion of innovation, supported by the National Science
Foundation (Grant G-36829). This support is appreciated.
ii VITA
July 8, 1947 ..... Born, Portsmouth, England.
1969 ...... B.A., Reading University, Reading, England.
1971 ...... M.A., Ohio State University, Columbus, Ohio.
1973 ...... Assistant Professor, Department of Geography, University of Oklahoma, Norman, Oklahoma.
PUBLICATIONS
"Diffusion Through an Urban System: The Testing of Related Hypotheses." With L.A. Brown. Tijdschrift Voor Economische En Sociale Geografie, Vol. 64, 1973
FIELDS OF STUDY
Major Fields: Social and Transportation Geography I
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ...... ii
V I T A ...... ili
LIST OF T A B L E S ...... vi
LIST OF F I G URES...... vii
CHAPTER
I. INTRODUCTION 1 Geographical Diffusion Research in Perspective The Organization of the Dissertation
II. A THEORY OF MACRO AND MESO SCALE DIFFUSION ...... 7 Diffusion at the Macro Scale Diffusion at the Meso Scale Diffusion at the Micro Scale Conclusions and Summary
III. THE DIFFUSION OF ARTIFICIAL INSEMINATION IN SOUTHERN SWEDEN . . . 38 The Innovation and Empirical Problem The Regional Setting Conclusions and Summary
IV. DESCRIPTIVE PROPERTIES OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH SOUTHWEST SKANE: AN AGGREGATE DATA ANALYSIS...... 46 The Data The Diffusion of Artificial Insemination: The Supply Perspective The Diffusion of Artificial Insemination: The Demand Perspective Conclusions
iv V. MODELS OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH SOUTHWEST SKANE: AN AGGREGATE DATA ANALYSIS...... 83 The Data Meso Scale: The Distribution of Adop ters Meso Scale: The Diffusion Strategy The Micro Scale: Demand and Adoption Conclusions
VI. DESCRIPTIVE PROPERTIES OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH A SAMPLE OF FARMERS: AN INDIVIDUAL DATA ANALYSIS...... 100 The Data The Pattern of Diffusion ^ ^Conclusions
VII. MODELS OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH A SAMPLE OF FARMERS: AN INDIVIDUAL DATA ANALYSIS .125 The Data A Model of the Time of Adoption A Causal Model of the Time of Adoption Conclusions
VIII. SUMMARY AND CONCLUSIONS...... 138 A Summary Some Critical Comments and Notes for Further Research
APPENDIX 1 ...... 144
APPENDIX 2 ...... 146
APPENDIX 3 ...... 147
BIBLIOGRAPHY ...... 150
v LIST OF TABLES
Table Page
1. Hypothesized Correlations from the Causal M o d e l ...... 136
vi LIST OF FIGURES
Figure Page
1. Stages of Diffusion ...... 4
2. Operating Costs Associated With the Public Good: Uniform and Step Cases . . 16
3. Change in Economic Rent: Large Q, Shallow Rent C u r v e ...... 22
4. Change in Economic Rent: Small Q, Shallow Rent Curve ...... 24
5. Change in Economic Rent: Large Q, Steep Rent C u r v e ...... 24
6 . Change in Economic Rent: Small Q, Steep Rent C u r v e ...... 24
7. Distribution of Adopters at Two Time Periods and Four Zones of the Public G o o d ...... 28
8 . Distribution of Adopters at One Time Period Given the Effect of the Spread of Information...... 33
9 . Distribution of Adopters at Two Time Periods and Four Zones of the Public Good. (Given Effect of Spread of Information)...... 33
10. Spatial Distribution of Adopters Given a Multi-Step Flow of Information . . . 36 11. The Communes of Malmohus La n ...... 40 12. The Distribution of the Initial Time of Adoption...... 50
13. The Relationship Between Percent Adopters and Time ( 1 - 4 ) ...... 52
vii 14. The Relationship Be tween Percent Adopters and Time (5-8) . 53
15. The Relationship Between Percent Adopters and Time (9-12) , 54
16. The Relationship Between Percent Adopters and Time (13-16) 55
17 . The Relationship Between Percent Adopters and Time (17-20) 56
18. The Relationship Be tween Percent Adopters and Time (21-24) 57
19 . The Relationship Between Percent Adopters and Time (25-28) 58
20 . The Relationship Between Percent Adopters and Time (29-32) 59
21. The Relationship Between Percent Adop ters and Time (33-36) 60
22. The Relationship Between Percent Adopters and Time (37-40) 61
23. The Relationship Between Percent Adopters and Time (41-44) 62
24. The Relationship Between Percent Adopters and Time (45-46) 63
25. The Dis tribution of a Values . . • » • 65
26. The Distribution of Adopters in ICommunes (1944) ...... 67
27. The Distribution of Adopters in Communes (1946) ...... 68
28. The Distribution of Adopters in Communes (1948) ...... 69
29. The Distribution of Adopters in Communes (1950) ...... 70
30. The Distribution of Adopters in Communes (1952) ...... 71
31. The Distribution of Adopters in Communes (1954) ...... 72
viii 32. The Distribution of Adopters in Communes (1956)...... 73
33. The Distribution of Adopters in Communes (1958)...... 74
34. The Distribution of Adopters in Communes (1960) ...... 75
35. The Distribution of Adopters in Communes (1962 ) ...... 76
36. The Distribution of Adopters in Communes (1963 ) ...... 77
37. The Distribution of b V a l u e s ...... 78
38. The Relationship Between the Percent of Adopters and Distance to Kavlinge . . . 80
39. The Distribution of Residuals From Equation ( 2 4 ) ...... 93
40. The Distribution of Residuals From Equation ( 2 6 ) ...... 98
41. The Location of the Sample Area .... 101
42. The Sample Area in D e t a i l ...... 102
43. The Distribution of Individual Adopters (1946 ) ...... 104
44. The Distribution of Individual Adopters (1947 ) ...... 105
45. The Distribution of Individual Adopters (1948 ) ...... 106
46. The Distribution of Individual Adopters (1949 ) ...... 107
47. The Distribution of Individual Adopters (1950 ) ...... 108
48. The Distribution of Individual Adopters (1951 ) ...... 109
49. The Distribution of Individual Adopters (1952 ) ...... 110
ix 50. The Distribution of Individual Adopters (1953 ) ...... Ill
51. The Distribution of Individual Adopters (1954) ...... 112
52. The Distribution of Individual Adopters (1955 ) ...... 113
53. The Distribution of Individual Adopters (1956 ) ...... 114
54. The Distribution of Individual Adopters (1957 ) ...... 115
55. The Distribution of Individual Adopters (1958 ) ...... 116
56. The Distribution of Individual Adopters (1959 ) ...... 117
57. The Distribution of Individual Adopters (1960 ) ...... 118
58. The Distribution of Individual Adopters (1961 ) ...... 119
59. The Distribution of Individual Adopters (1962 ) ...... 120
60. The Distribution of Individual Adopters (1963 ) ...... 121
61. The Distribution of Individual Adopters (1964 ) ...... 122
62. Residuals from Equation (28) ..... 130
63. Residuals from Equation ( 2 9 ) ...... 132
64. A Causal Model of the Time of Adoption .134
x CHAPTER X
INTRODUCTION
This dissertation reports on empirical work carried out within the context of a theory of diffusion of innovation originally proposed by Brown (1973). The theory, which will be described at length in Chapter 2, is oriented towards supply related aspects of diffusion.
This is in contrast to most previous work in geographical diffusion theory, which has been oriented towards the demand behavior of individuals. The present theory involves two components; the establishment and location of diffusion agencies, termed the macro scale problem, and the strategy by which a diffusion agency reaches potential adopters, termed the meso scale. The theore tical framework will be evaluated using data of the diffusion of artificial insemination of cattle amongst farmers in southwest Skane, Sweden, over a period of twenty-one years.
Geographical Diffusion Research in Perspective
Before entering into a discussion of the theoretical framework provided by Brown, it will be instructive to place previous diffusion research related to the macro and
1 meso scales into perspective.
Throughout this study we are concerned with the
diffusion of innovations from a locational point of
view (Haggett, 1965; Brown and Moore, 1970). Moreover,
there is an overriding concern for explanation of spatial
patterns resulting from diffusion. Brown and Moore write, for example, that in this approach ’attention
turns to the identification of the generative processes
by which the observed locational pattern of a given
phenomenon comes into existence’ (Brown and Moore, 1970,
p. 122).
A framework in which to provide such a perspective
is given by Harvey (1969). This is particularly useful,
since it is based on approaches to explanation. Harvey
suggests that in dealing with the evolution of spatial distributions, there are four means of explanation:
through verbal narrative, by reference to stage, by reference to hypothesized process and by reference to ex
plicit process.
These forms are not mutually exclusive, but are
rather emphases of approach. Also, one should realize
that they represent a continuum from descriptive to
explanatory approaches, i.e. increasing rigor of explana
tion. Diffusion research at the macro and meso scales will here be evaluated within the context of the second,
third and fourth means of explanation. Explanation by reference to stage in diffusion is
exemplified by the work of Hagerstrand, who postulated
the existence of three stages, primary, diffusion and
condensing, to the diffusion of an innovation from a
single innovation center (Hagerstrand, 1952). The same
stages were also employed to explain diffusion through
a system of centers (Hagerstrand, 1952, 1966). The
major concern in this work is the demand for and the
adoption of an innovation by individuals. Figure (1)
indicates the form of each of these stages for diffusion with respect to one center. In the primary stage,
adoption is prevalent in the vicinity of the innovation
center. During the second stage, adoption has spread
outward to the more distant areas, whilst in the final
stage, diffusion has slowed down and adoption occurs in
all areas.
Within this particular mode of explanation, there
Is less concern with the supply of the innovation to
the center or to the centers of the system, an integral part of the diffusion process.
Similar modes of explanation have been used by
Griliches and Casetti and Demko (Grillches, 1957; Casettl
and Demko, 1969; Demko and Casetti, 1970). Griliches
employed a three stage cycle similar to that used by
Hagerstrand for diffusion within a system of centers. He
also attempted to Identify those factors that were 4
PRIMARY
DISTANCE FROM INNOVATION CENTER
Ui »- CL o DIFFUSION o <
O
UJZ U a t UJ a .
UJ > DISTANCE
3 s D
U VJ00 CONDENSING DISTANCE FIGURE Is STAGES OF DIFFUSION; PRIMARY, DIFFUSION AND CONDENSING influential at each stage, however. The model developed by Casetti and Demko resembles the one of Hagerstrand, in which diffusion occurs from a single center. The model can be used to test hypotheses about the existence of diffusion and of the stages involved. Explanation by reference to hypothesized process is another approach to this problem of explanation of diffusion patterns. Hagerstrand's work^whlch again is oriented toward the demand for the innovation, hypothe sized the significance of interpersonal communication as the major factor influencing adoption (Hagerstrand, 1952, 1965, 1966, 1967). Other work shows a concern for the supply of the innovation and those factors that influence this decision-making behavior. A theoretical thrust in this direction is provided by Brown (1967, 1969, 1973; Brown and Cox, 1971; Brown and Lentnek, 1973). Empirical studies on the diffusion of such innovations as hybrid corn, crematoria, shopping centers and various entre preneurial and industrial Innovations in several countries have provided strong evidence for the importance of expected profitability and to a lesser extent accessibility factors in this supply problem (Griliches, 1957; Hanham and Brown, 1973; Cohen, 1972; Pedersen, 1970). There do not appear to be any studies in the literature that employ explanation by reference to explicit process. This would involve the in-depth analysis of case studies of diffusion with the use of questionnaires for each decision-maker contributing to the diffusion of the inno vation. The Organization of the Dissertation. The theoretical framework derived by Brown, under the titles macro and meso scales of diffusion, is described in Chapter 2. This framework has been extended and several models proposed. In the same chapter, the demand aspects of diffusion and corresponding individual adoption behavior is also considered. This is here termed the micro scale. Chapter 3 provides a description of the innovation, the empirical problem and how it relates to the theore tical framework, together with a regional setting for this problem. Chapters 4 and 5 provide a descriptive and analytic approach to relating the empirical problem to the theoretical framework. Both are concerned with the diffusion of artificial insemination of cattle through the communes of southwest Skane, and thus employ aggregate data of adoption. Chapters 6 and 7 also provide descrip tive and analytic approaches to this problem, but are concerned with diffusion of artificial insemination amongst a sample of individual farmers, and hence use data relevant only to those individuals. The final chapter, 8, provides a summary of the major findings in the study, together with a set of conclusions and suggestions for further research in this area of diffusion. CHAPTER 2 A THEORY OF MACRO AND MESO SCALE DIFFUSION Brown recognizes three scales in the diffusion of an innovation, macro, meso and micro (Brown, 1973). These scales do not necessaxvily reflect spatial scales, hut rather distinguish sets of decision-makers. The macro scale is concerned with the establishment and loca tion of diffusion agencies. The decision-makers at this scale affect spatial aspects of the supply of the innovation. The meso scale is concerned with the strategy by which a diffusion agency reaches potential adopters. This involves establishing an interface between one set of decision-makers affecting supply and another set concerned with demand. The micro scale is concerned with the decision-making behavior of potential adopters, and is therefore oriented to demand factors. Each of these scales will be discussed in turn. Some aspects of each will be emphasized more than others, since they bear more heavily upon the particular empiri cal problem. This will be pointed out at each step. The sections on the macro and meso scales will draw upon the work of Brown in large part (Brown, 1973; Brown and Lentnek, 1973). 7 8 Diffusion at the Macro Scale. Two types of diffusion are recognized at this scale, mononuclear and polynuclear. In the former, a single propagator is responsible for the decision to locate a set of diffusion agencies. In the latter, the responsibility for locating these agencies is decentralized and the deci sions carried out by more than one propagator. As such, certain aspects of the decision process vary between the two cases. For the purposes of this empirical study, however, only the mononuclear case is discussed. The propagator locates the diffusion agency by applying a decision rule to a preference or utility function. Such a function assigns individual utility to an outcome, in this case the outcome of placing an agency In any given location. Decision rules and utility functions do vary between individuals, but often decision-makers such as propagators can be classified Into types, with character istic utility functions and employing certain decision rules (Isard and Dacey, 1962; King and Jakubs, 1970). In many instances the utility of locating an agency to a propagator is its future profitability. This In turn Is dependent upon future revenue and costs associa ted with that location. Revenue is a function of, among other things, sales potential, number of potential adop- tors, per capita income and cosmopoliteness. Depending upon the particular innovation, there may also be a threshold upon the size of the center in which the agency may be located. Costs will be a function of poten tial adopter density and accessibility of the agency to the parent center. These factors will affect distribution and service transportation costs. Profitability need not be the major criterion in the utility function. Utility may, for example, be a function of social welfare. This is likely to depend, moreover, upon the character of the innovation. In the case of certain public goods, the utility of locating a diffusion agency could be measured in terras of social welfare rather than profitability. Although , theoretically,it is possible for propagators to develop objective utility functions and assign utili ties to all locations, it is more likely that biases arise through variations in perception. The propagator^ awareness space will be determined to a large extent by the amount of information available to him, together with his past experience. Not only will the number of potential locations be less, but so will knowledge of the attributes of those locations. The marketing surface therefore becomes a perceived surface, and the utility function a subjective one. Assuming a spatial bias in the availability of information, one would expect a similar bias in the potential agency locations for which the utility function is relevant. The types of decision rules that may be applied by propagators likewise are numerous. These have been outlined elsewhere (Isard and Dacey, 1962; King and Jakubs, 1970). The propagator may be a maximizer or a satisficer, he may maximize utility or expected utility, and so on. The particular rules used will depend upon such factors as the goals of the propagator, the availability of capital and the objectivity of the utility function. The latter suggests that the utility function and the decision rule may not be independent of each other. Finally, the utility function and decision rule of the propagator will both be influenced by the existence of a set of agencies that have been previously located. Such agencies will not only afford the propagator with more information, and hence enable him to re-evaluate his utility function, but it will also limit the number of agencies to be located and to some extent force the • propagator to channel the innovation into previously established directions. The decision process discussed thus far is essentially static. It assumes that preferences are consistent through time and that there is no incentive to change the deci sion rule. The individual propagator is assumed to have achieved an asymptotic or equilibrium level of learning. In reality this will generally not be true. A propaga tor will learn about further potential locations for 11 his agencies, either by trial and error or by systematic search procedures. As a result, his utility function will become more objective and he may also become confident enough to change his decision rule. A Model of Mononuclear Diffusion. Assume that an individ ual propagator wishes to locate a diffusion agency, such that he will maximize future utility. Further assume that utility is a function of profitability, which is defined as benefits minus costs. Therefore kU “ U (P) » P Where U is utility for propagator k, and P is profitability. Also P = (Bte“rt - Cte"rt) (1) Where B is benefits C is costs t is time and r is a parameter^-. The future profitability of a given location i is then defined as (Bite”rt - C£te-rt) dt (i » l,2,...n). (2) Where T is some point in time in the future. Since the propagator is assumed to maximize future utility, he will choose that location which maximizes *1 This model is derived from a model of migration from a human investment point of view (Comay, 1972). 12 (2), i.e. Maxi £ ^ (Blte"r,: - Cite"rt) dt] (3) If more than one agency is to be located, the next most profitable location will be chosen, and so on. According to the previous theoretical discussion of mononuclear diffusion, B and C may be further defined. Hence Bi " B Where is the number of potential adopters, x12 Per capita income, and X^3 is cosmopoliteness. Likewise Ci =* C(X^^, X^^) (5) Where X ^ is potential adopter density and X^^ distance to the propagator's center. If we allow for the fact that propagators vary In their perception of the marketing surface, then the model may be altered accordingly. Assume that a propagator (k) is aware of only n' potential locations, where n ? n, and n is the total number of locations 1. Also, assume that the propagator perceives m 1 attributes concerning these locations, where m' < m, and m are the real and objective attributes of the locations. Let W ^ be a vector of real attributes j for i locations. Let be a vector of the perceived attributes, consisting of both benefits and costs for propagator k. The utility function for individual k Is therefore 13 a composite of weighted attributes, kUi 3 [Ckaj> * (kvij>] Where is the relative importance of attribute j for individual k. is in this instance a subjective utility 9 function for propagator k. Diffusion at the Meso Scale. Two broad types of meso scale diffusion are recognized, monophasic and polyphasic. The former is distinguished by the fact that potential adopters are influenced in their decision to adopt only by factors occurring prior to adoption. Polyphasic diffusion is characterized by influential factors occurring both prior to and after adoption. With this in mind, the strategies employed by the diffusion agencies are seen to vary according to the characteristics of these two types of diffusion. The pattern of diffusion at the meso scale therefore depends upon the strategies and decisions of the agency in reaching the potential adopter, and upon the decisions made by the latter. Obviously the decision to adopt is constrained by the decisions of the agency. Polyphasic diffusion is subdivided on the basis of those factors that influence the decision to adopt subsequent to adoption. In one case, such factors are ^ h e reasoning behind this model is derived from Demko and Briggs (1971). 14 the cost of transporting a good in response to the use of the innovation. Generally we assume the good to be trans ported to market, although it may only be to an intermediate center. This type of polyphasic diffusion is termed the 'transport dependent case*. In the alternative case, these factors are the operating costs associated with infra structure or service necessary for the functioning of the innovation. This type is termed the "public good dependent 3 case'. In the last type, we may, moreover, distinguish between a consumer good innovation and one that is an input to an ongoing economic process. In view of the particular empirical problem with which we are concerned, the following discussion is oriented toward an innovation that is an input to an ongoing economic process and the public good dependent case of polyphasic diffusion. Assume the following: (1) a hinterland region of a single agency in which are located a number of potential adopters, (2) the potential adopters are producers with given ■^A more apt term is probably 'collective good.' A collective good arises whenever some segment of the public collectively wants and is prepared to pay for a different bundle of goods and services than the unhampered market will produce. It may be privately or publicly provided. When the coordinating mechanism for providing it invokes the powers of the state (or a government), then the good is a public good. (See Steiner, 1969, for an extensive discussion on this topic. He also suggests that co-ops, unions, clubs and trade associations are all examples of private organizations that arise in response to collective demand for a private collective good or service.) Bearing this in mind we will however maintain the use of the term public good. 15 production functions, (3) the aim of the agency is to induce the potential adopters within its hinterland to adopt an innovation, (4) the innovation is an input to an ongoing economic activity, (5) the adoption of the innovation by producers is dependent upon the availability of a public good or infrastructure, (6) the public good is not immediately made available to all potential adopters, but is provided in stages. Given the above, there is one critical factor that affects the diffusion of the innovation, and that is the operating costs associated with the public good. In that portion of the hinterland in which the public good is avail able, operating costs will be uniformly low or mildly stepped. Where it is not available, such costs will be exceedingly high (see Figure (2)). As the penetration boundary of the public good is pushed further outward from the agency, operating costs for potential adopters subse quently diminish. This infrastructure may be provided by the agency Itself or by an independent entity. If the latter is the case, then the agency's supply strategy will depend upon the strategy of this independent entity to some extent. If, on the other hand, the former is the case, the agency has more direct control of the diffusion of the innovation. The strategy of the agency in reaching potential adopters will therefore be reflected in the extent to which and the time 16 CO Is u° £ o i-IQC I s* DISTANCE TO AGENCY i- “I— s* DISTANCE FIGURE 2: OPERATING COSTS ASSOCIATED WITH THE PUBLIC GOOD: UNIFORM AND STEP CASES 17 taken to make the public good available in the hinterland. The agency may direct the diffusion pattern of the innovation by making the public good available only in certain areas and to particular potential adopters. The strategy of the agency in this matter may be comparable to that of the propagator in locating the agencies. The location of the public good may be governed by a utility function, the independent variable of which is profitability, social welfare or some other criterion. If it is profitability, there are certain benefits associated with the location of the public good and subsequent adoption. Such benefits may be a function of, among others, number of potential adopters, per capita income and cosmopoliteness. Similarly, there are certain costs such as the cost of establishing and servicing the public good. These may be a function of potential adopter density and accessibility of the public good to the agency. As in the case of the propagator, the individual acting as the agency may vary as to his perception of the marketing surface. A parallel argument can be made, for the existence of a subjective utility function for the agency, in which perceptual biases are a function of information and experience, i.e. the extent of learning. Similarly, the decision rule used by the agency will depend upon such factors as the goals of the individual 18 agent, the availability of capital and the objectivity of his utility function. Finally, the location of the public good will be influenced by its previous location. As in the case of the propagator, the strategy of the agency should be viewed as being dynamic. It is likely to change with time and through learning. A Model of Meso Scale Diffusion. Such arguments as those presented above suggest that the agency is subjected to a comparable problem of decision making and constrained by similar factors, as is the propagator at the macro scale. This appears to be the case for the diffusion of an innovation which is an input to an ongoing economic activity and which requires infrastructure for it to function. Given the above, it is suggested that a decision model similar to that of the propagator's be applicable to the agency. Utility for agency k is therefore defined as in equation (1), and the location i in which the public good will be located will be determined by equation (3). A modification of the model due to perceptual biases on the part of the agency may similarly be developed. If the agency controls the location of the infra structure, and assuming that the benefits or revenue resulting from adoption are equal throughout the agency's hinterland, then one would expect the public good to be provided at first in the Immediate vicinity of the agency 19 due to service costs. With Increased capital and a desire to Increase profits, the public good will then be provided in stages toward the periphery of the hinterland. A model of the distribution of adopters is now developed. Let us assume that operating costs are uniformly low from the location of the agency to the penetration boundary of the public good, and thereafter exceedingly high. Also, assume that the price of the innovation, acquisition and opportunity costs and the availability of information concerning the innovation is everywhere constant. Assume that all potential adopters aim to maximize profit in their production, and hence do not vary in their decision making behavior. Incentive to adopt is a function of the expected Increase in net profit from the production process after adoption of the innovation, and this increase will result if the reduction in production costs through the use of the innovation more than offsets the added operating costs of the public good. A reduction In production costs will be expected if the innovation is either capital or labor saving. Let H be the change in net profit from the production process after adoption and R the net profit prior to adoption. R + H - R' Is the total net profit after adoption. If H > 0, there is assumed to be an incentive to adopt the innovation. 20 Now, H ="Ma - q) E (ofs£s*) (6) |(a - Q) E (s* Where a is the savings in production cost per unit of product, E is the yield of product per unit land area, q is the operating cost per unit of product of the public good, from the agency to the penetration boundary, Q is the operating cost per unit of product of the public good, from the penetration boundary outward, s is the distance of the adopter from the agency, s* is the distance of the penetration boundary from the agency. Provided that (a - q) or (a - Q) is greater than zero, then H > 0 and there is incentive to adopt. How ever, Q is assumed to be infinitely large, and so it is unlikely that (a - Q) > 0. It follows that there is incentive only between the agency and the penetration boundary, and this will only occur if q is sufficiently small not to exceed a. Since dH/ds “ 0 for (0 <_ s <_ s*) , there is evidently no spatial variation in the incentive to adopt. Although we have assumed that the incentive is constant,provided that H > 0, one can postulate that the incentive is itself a function of the magnitude of H. 21 There would, however, again be no spatial variation in the incentive to adopt. R, the net profit prior to adoption is now defined as R = R(s) - E(p - c) - Eks (0 <. s) (7) Where p is the price per unit of product at the market center, c is the production cost per unit of product, k is the transport rate per unit of product. s is the distance from the producer to market. Note that R also defines the economic rent of land at any given distance from the market. If we make the assumption that the agency is located in the market center, then the net profit after adoption is R' B R + H B [ E(p - c) - Eks + E(a - q) (0 <. s £ s*) (8) E(p - c) - Eks + E(a - Q) (s* < s) Rearranging terms, equation (8) becomes R* = R + H = [ E[p - c + (a - q)] - Eks (0 <. s <. s*) (9) E[p - c + (a - Q) ] - Eks (s* < s) Note that over the distance range (.0 <. s <. s*) , dR'/ds =• dR/ds =* Ek, and that, assuming equations (7) and (9) to be linear functions, the intercept of these two functions differs by the constant E(a - q). Figure (3) illustrates the form of equations (7) and (9) where (a - q) > 0 and (a - Q) < 0 . 22 Q a z < I/) t- o u u o z S 1“ o < z DC. U-l o Q. u o + 0 DISTANCE TO AGENCY FIGURE 3: CHANGE IN ECONOMIC RENT: LARGE Q, SHALLOW RENT CURVE Two major assumptions, which strongly Influence the spatial distribution of adopters to this point, are that the operating costs of the public good beyond the penetration boundary is exceedingly high and that the surface of economic rent or net profit is everywhere positive in the region. The operating costs Q, however, nay vary from exceedingly high to relatively low, albeit greater than q. The surface of economic rent likewise may vary, from being positive throughout the entire region to only being positive within a short distance of the agency. This may be due to high transport or production costs or a low price, for example. Since we have consid ered the case of very high operating costs Q and positive economic rent throughout the region, we will further con sider three alternative situations. These are, low Q and high rent surface, high Q and low rent surface and low Q and low rent surface. In the first case, since Q is relatively low, (a - Q) may be positive, although (a - q) > (a - Q). Figure (4) indicates this situation. Notice that the incentive to adopt is positive beyond the penetration boundary, although it is not as great as it is before the boundary. The rise in economic rent due to innova tion adoption has extended the zone of production from that distance where R « 0 to where R f « 0. The number of new producers brought into the system will therefore depend upon the value of Q. If adoption depended upon ECONOMIC RENT AND 0 0 FIGURE IUE : HNE N CNMC RENT: IN ECONOMIC CHANGE 5:FIGURE IUE : HNE INRENT: ECONOMIC CHANGE 4:FIGURE DISTANCE DISTANCE DISTANCE 6 CAG I EOOI RENT: IN ECONOMIC CHANGE : ML Q SEP ET CURVE STEEP RENTSMALL Q, AG Q SEP ET CURVE STEEPRENT Q,LARGE ML Q SHALLOW CURVESMALL Q,RENT 25 the extent of the incentive, then the probability of adoption would be greater up to the penetration than beyond it. The difference in probability would also depend upon the difference in the incentive. In the second case, since Q is high, (a - Q) will be negative. However, since the economic rent surface is low, adoption takes place only to the distance where R' = 0 (see Figure (5)). This distance may be less than s*, the penetration boundary. Since the rent surface has been raised though, new producers will be brought into the market. The third case, illustrated in Figure (6), results in a similar distribution of incentive. Although Q is low, this is insufficient to raise R 11 above zero beyond the penetration boundary. New producers are brought in up to the same distance as in the previous case, and this is less than s*. Although the point will not be discussed at length, the level of the operating costs will Indirectly affect the supply and price of the producer's final product. This will be so, since new producers may be brought Into the system and supply will rise and prices fall. This in turn may regulate the adoption of the innovation, since producers near the periphery of the region will then have less than zero rent. Indeed, this may be postulated as a major reason for the decline often found in the final adoption surface at distances furthest from the centers 26 from which the innovation originated (see Morrill, 1970, for example). Moreover, the agency could employ a policy of setting operating costs at certain levels in order to regulate the adoption of innovation. Given the strategy of the agency in providing the public good and given that all potential adopters have the same production functions, preferences and aim to maximize profits, one would expect the distribution of adopters to be uniform. In particular, the distribution will be uniform from the agency to either the penetration boundary or to the distance at which R* = 0, from whence there will be no adoption. Hence A ° 1 A (H) (0 < s < s ’) (H > 0) (10) [ 0 (s’ < s) (H < 0) Where A is the percent of potential adopters who have adopted and s' is that distance from the agency where R' “ 0. Over time the public good will be extended outward into the agency hinterland. If this occurs in stages, then we will expect a succession of zones in which the public good became available. Theoretically this pattern will be one of concentric zones; in reality, of course, there are likely to be directional or sectoral biases which distort the more prominant distance bias. Alter native strategies of the agency, pre-existing infrastructure, competing agencies, physical barriers and spatial varia tion in potential adopter demand are some of the factors 27 which may create such distortions. If the penetration boundary has proceeded outward in stages, then the distribution of adopters at any given time will be of the form, (0 < s < s ’) (H± > 0) (11) (s' < s) (Hi < 0 ) (i = 1 , 2 , . . . , n) Where n refers to the number of stages or zones and refers to the change in net profit associated with each zone. It is evident that a function such as that in equation (11) would be a stepped function of distance. Figure (7) illustrates, diagramatically, the form of such a function, in which the public good has been extended outward in several stages. It is assumed in Figure (7) that Q is very high at each stage, and that the economic rent surface is also high. Diffusion at the Micro Scale. The discussion thus far has emphasized essentially the supply related decisions at the macro and meso scales. Such decisions are obviously not unrelated to the demand from potential adopters. For the purposes of modelling the distribution of adopters in the previous section, given the agency's strategy, it was necessary to make a number of assumptions concerning potential adopter behavior. At the micro scale, attention is 28 Time t______CEILING LEVEL t -1 t-1 at a. O Q < o o' t-1 »-l -t:------r:------r — — ■■■■■!■ S] s2 s3 s DISTANCE TO AGENCY FIGURE 7: DISTRIBUTION OF ADOPTERS AT TWO TIME PERIODS AND FOUR ZONES OF THE PUBLIC GOOD 29 turned toward the decision making behavior of potential adopters; what are its components, what factors influence it and how it varies through space. The potential adopter must first be aware of a problem or stress, the solution of which may be the adoption of an innovation. Stress may in fact be caused prior to awareness of the innovation, or alternatively may result from an awareness of it (Campbell, 1966). Part of the strategy of an agency, for example, may very well be to create such stress among potential adopters. Motivation to reduce stress and resolve the problem will depend upon the aspirations of the individ ual decision maker, which in turn may be expected to depend upon his goals and values. If stress has occurred prior to awareness of the innovation, the individual will undertake a search for a possible solution. This takes the form of information gathering, and the results that it produces will depend upon the individual's personal and impersonal network of contacts and the motivation available to extend these. Following awareness of an innovation (or inno vations) as a possible solution, the individual will attempt to evaluate its utility. This stage of the decision process will depend upon the individual's perception of the innovation, its characteristics and how it relates to the original problem. A further search 30 procedure will be carried out, gathering information so that an evaluation can be made.^ It may also be possible to conduct a trial as part of the evaluation procedure. This entire stage of the decision making behavior of the individual is essentially a learning process. The final stage in this process is the decision whether to adopt or not, or possibly which innovation to adopt from a number that are available. This is the final choice, and it may be conceptualized as the application of a decision rule to a preference scale. This scale is defined by a subjective preference or utility function, which is in turn determined by the previous learning process and past experience. This scale may, for example, be a function of the expected profitability of investing in the innovation. As in the case of the propagator and agency, the decision rule varies between individual potential adopters; it may be to maximize utility, maximize expected utility, choose the first satisfactory alternative (i.e. make the decision to adopt, provided that expected utility of the ^Although sociologists have recognized the importance of various Information sources at different steps In the decision process, the flow of information through Interpersonal channels is regarded as a static phenomenon. It is either assumed to flow in a wavelike fashion or as a two or multi-step flow. It would appear to the more realistic to suggest that an individual decision maker may attempt to extend these through various search procedures at particular steps in the decision process (see Cox, 1969, for a discussion on the genesis of acquaintance networks for example). 31 innovation exceeds a threshold of utility), and so on. If the decision is made to not adopt, then the potential adopter accepts the present level of stress. If we assume the preference scale to be a function of profitability, there are a number of benefit and cost factors which may be expected to affect this. Besides the reduction in production costs and the imposition of operating costs discussed in the previous section, profit ability will be influenced by changes in the price of the final product, costs of acquiring the innovation, opportunity costs relative to those associated with alternatives and any increase (or decrease) in transport costs resulting from the use of the innovation. Provided that the Innovation Is capital or labor saving, the Incen tive to reduce production costs may be especially acute if the price of a particular input is high or supply is low. The importance of individual goals, aspirations and motivation in influencing the adoption decision may be reflected in or caused by a number of personal charac teristics of the potential adopter. These have been discussed at length in the sociology literature (see Rogers, 1971 and Jones, 1966). For example, earlier adopters tend to be younger and better educated, have higher incomes and social status, have larger businesses and are more specialized in their employment, have more contact sources outside of the community in which they 32 live, participate more in organizations, are more urban- oriented and interact with others more than average. A Modified Distribution of Adopters Model. What conse quences will result if we relax the assumption in the model of the distribution of adopters that all potential adopters exhibit similar decision making behavior? If we drop the assumption of equal information sources, and suppose that information concerning the innovation is spread outward from the agency, then at any given time the distribution of adopters will be a decreasing function of distance from that agency, i.e., (0 This is illustrated in Figure (8) for the case In which operating costs (Q) from the penetration boundary outward are very high and the surface of economic rent is also high. Over time, and given that the penetration boundary is extended outward in stages, the distribution of adopters at any given time will be of the form, s) (0 < s i s') (H± > 0) (13) (s' < s) (H^ < 0) This function is also stepped, although for each step, A is a decreasing function of distance. Under these conditions, we might expect diffusion to exhibit 33 UJ CL o a < DISTANCE TO AGENCY FIGURE 8 : DISTRIBUTION OF ADOPTERS AT ONE TIME PERIOD GIVEN THE EFFECT OF THE SPREAD OF INFORMATION 34 through time and within any given zone, the stages in the diffusion process that were proposed by Hagerstrand (1952). Figure (9) illustrates the form of such a distribution where both Q and economic rent are assumed to be high. If, on the other hand, we hypothesize the existence of a two or multi step flow of information amongst the C potential adopters in the agency hinterland , we expect the distribution of adopters to reflect a degree of clustering, perhaps with a trace of distance decay from the agency. This distribution will of course be con strained by the penetration boundary of the public good (see Figure (10)). The existence of spatial variation in a number of other factors will detract from the simple distributions outlined so far. Variation in decision making behavior and its components, such as preferences, perceptions and decision rules, and variations in the factors that influence such behavior, such as personal characteristics and profitability factors, will all result in varied adopter and diffusion patterns. At the present, there is too little evidence or theoretical work to justify the creation of hypotheses regarding the spatial nature of the factors and their effects outlined above. ^This would occur if there existed a degree of acquaintance circle bias (see Brown, 1968). 35 OtC/7 (—UJ a. O a < o t-1 DISTANCE TO .AGENCY FIGURE 9: DISTRIBUTION OF ADOPTERS AT TWO TIME PERIODS AND FOUR ZONES OF THE PUBLIC GOOD. (GIVEN EFFECT OF SPREAD OF INFORMATION) 36 Agency Adopters FIGURE 10: SPATIAL DISTRIBUTION OF ADOPTERS GIVEN A MULTI-STEP FLOW OF INFORMATION 37 Generalizations such as these have not as yet been estab lished. We might surmise, however, together with Wolpert and Found, that spatial clustering of similar decision behavior might arise because of similar information sources and imitative behavior (Wolpert, 1964; Found, 1971) .6 Conclusions and Summary. A theoretical framework for the diffusion of innova tion has been outlined. The decision makers at the macro scale are concerned with the supply of the innovation in the form of diffusion agencies, whilst those at the meso scale are concerned with reaching potential adopters from the agency. Individual demand and adoption behavior is considered at the micro scale. Simple, but compara ble models of the supply location decision were derived for the macro and meso scales. A model of the individual adoption decision together with a model of expected distribution of adopters was derived for a number of alternative conditions. Finally, the effect of variation in information availability on the model of the distri bution of adopters was explicitly considered. In this context, Golledge makes reference to the possible utility of Guthrie's learning theory and the traditional use of contiguity as an explanatory variable in geography. (Golledge, 1969). CHAPTER 3 THE DIFFUSION OF ARTIFICIAL INSEMINATION IN SOUTHERN SWEDEN In the previous chapter, a theoretical framework for diffusion at the macro and meso scales was discussed. Using this as a basis, a number of models were developed and a section discussing the problem of diffusion at the micro scale added. Emphasis was placed on the discussion of only certain aspects of diffusion at these scales, because of the particular empirical problem with which this report is concerned. This chapter is divided into two major parts. The first describes the innovation, the empirical problem and how it relates to the theoretical framework. The second provides a regional setting for this empirical problem and describes the study area. The Innovation and Empirical Problem. The innovation with which we are concerned is the artificial insemination of cattle. In particular, diffu sion of this innovation has taken place in southwest Skane, Sweden, since 1944. It has been the policy of the Swedish government to establish regional associations, whose task it is to stimulate the adoption and diffusion 38 39 of artificial insemination of cattle amongst farmers. This was accomplished by the setting up of regional agencies, and may be regarded as a supply problem within the diffusion process. However, the decisions and factors affecting the location of these agencies is not the pro vince of this report. The location of agencies other than the one in Skane are unknown. The regional agency in this case was established in 1944 in Kavlinge, Malmohus Lan, and the full title of the association was the Kavlingeortens Serainforening. Figure (11) illustrates the location of the towns and communes in this province. The agency generates diffusion and provides the arti ficial insemination service to farmers who join the asso ciation. The means by which this is accomplished is to employ and authorize veterinarians in the region to imple ment the service. Each veterinarian has an area to serve, whilst they are serviced from the agency where the bulls are centrally located. This element of diffusion too is regarded as a supply problem. Moreover, the innovation is an input to an ongoing economic activity, the adoption of which is contingent upon the availability of a 'public good', namely the veterinarian and the service he provides. In 40 £Ko^otP / Odalsra /Morarp Norra Frosta Ostra Fro sto fAanstofp ^menh SkanorMe K/agitorp Falsterbo FIGURE 11: THE COMMUNES OF MALMOHUS LAN 41 summary, therefore, the diffusion of artificial insemin ation at this scale is treated here as the public good dependent case of polyphasic diffusion. It must be pointed out, however, that some confusion may exist since it is possible to argue that the head quarters of the association is the propagator rather than the agency. Subsequently, the policy of the prop agator is to locate agencies which would be the veterin arians. These in turn possess strategies for reaching potential adopters. On balance, however, and especially due to the fact that artificial insemination associations were established regionally, the initial argument appears more plausible. A Short Regional History of the Innovation. The Kavling- eortens Seminforening was established in the town of that name in 1944, Prior to the existence of this Innovation, farmers in the region had tended to rely on the services of bull associations for' the insemination of their cattle. The precise strategies of the agency in Kavlinge are unknown, although the use of authorized veterinarians with service routes to reach potential adopters is known. Also, it is reported that the agency made agreements with groups of farmers in certain parts of the region to supply the artificial insemination service. The 1946 yearbook, for example, reports two such agreements with farmers near Malmo and near Fars (Kavlingeortens 42 Seminforening yearbook, 1946). This same yearbook also describes the construction and renting of labora tories and cattle sheds in Kavlinge, pointing to central ization in the organization of the agency. Between 1946 and 1951, the agency was relocated in Lund, and had changed its name to Sydvastra Skanes Seminforening (the Southwest Skane Artificial Insemination Association). The precise reasons for this change are not available at present, although it can be noted that Lund is a larger, university town, more centrally located in the Southwest Skane region and certainly possesses more direct communications with other parts of the region. Naturally this would be of importance in establishing and servicing the veterinarians (i.e. the public good). The agency remained in Lund until at least 1964, the last year for which data is available. The Regional Setting. The Southwest Skane region is a particular distinctive one in Sweden. Its character and historical development are of interest not only in themselves, but also because they might afford some clues toward an understanding of the diffusion of an Innovation such as artificial insemin ation within the region. The fertile soils of moraine origin, its location 43 1 2 and historical tradition and urban growth , have all contributed to the development of an intensive agricul tural system in the region (Millward, 1964). The farms are the largest in Sweden, averaging just over twenty hectares, as well as being the most highly mechanized. The industry’s major products are cereals, sugar beets, vegetables, fruit and various dairy products. The major breed of cattle in the area is the Swedish Lowland variety, which apparently gives high milk yields (Somme, 1960). One major reason for the development of agriculture in Southwest Skane, and one with important implications for the present study, is that it was the entry point for many innovations that had spread from other parts of Europe. After the enclosure of the open fields and redistribution of farmsteads from the villages in the nineteenth century, the efficiency of production increased rapidly. In large part this was due to research on plant breeding and technical improvements in dairying and slaughtering. These led to large agricultural surpluses, which were made available to the market for the first time in the late nineteenth century. One consequence of ■^Neolithic farmers migrated from Denmark into this area for example. 2 This is the most densely populated area in Sweden. 3 The area has the highest density of tractors and combine-harvesters in the country (Somme, 1960). 44 this was the growth of the private entrepreneur* or middleman, who would take a large share of the profits in the marketing of this surplus. To counteract this trend in countries such as England and Germany, the concept and operation of the cooperative was established. This innovation itself spread through Denmark and into Southwest Skane, and thence to other regions of Sweden (Somme, 1960) . The characteristics of Skane, therefore, were such that the region was receptive to innovation. A further consequence of this was that the income effect derived from these was more likely to be apparent in Skane than in other regions. Conclusions and Summary. In the succeeding chapters, data on the diffusion of artificial insemination in Southwest Skane will be used to empirically evaluate the theoretical framework outlined in Chapter 2. It is assumed that the establishment of the artificial insemination agency in Kavlinge and Lund is a macro scale problem. Due to lack of data, the utility of this part of the theoretical framework in explaining diffusion will not be evaluated. The loca tion of the agency is taken as given. The reasons for the shift in location from Kavlinge to Lund can also only be surmised. The establishment of veterinarians and their service 45 routes, and the strategies by which the agency located these, is a meso scale problem. Aggregate data on the adoption of artificial insemination by farmers in the com munes of Malraohus Lan will be used to evaluate the theoretical framework regarding this scale. The same data will also be used to analyze variations in poten tial adopter demand, or in other words the micro scale problem. Finally, the supply and demand aspects of diffusion will also be analyzed with the use of data on individual adopters. Details regarding the data and data sources will be presented in the introductions to the chapters in which they are used. CHAPTER 4 DESCRIPTIVE PROPERTIES OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH SOUTHWEST SKANE: AN AGGREGATE DATA ANALYSIS In this chapter, the time and space trends of the diffusion of artificial Insemination through the communes of Malmohus Lan are described. The spatial aspects of the supply of the innovation, namely the macro and meso scales, are considered first. For reasons to be ex plained shortly, this will be treated as being synonymous with the initial time of adoption within each commune. The time and space trends of Individual demand for and adoption of the innovation, namely the micro scale, are considered second. This is related to the rate of adop tion within each commune. The description of these trends is accomplished with the use of graphs and maps. Apparent regularities in these trends are pointed out, and an attempt is made to associate these with explanatory variables. The use and results of statistical models for the same purpose is, however, presented in the succeeding chapter. Before describing such trends, the data used in the chapter and its sources is outlined. 46 47 The Data. Besides the location of the towns and communes for which the data Is available, the sole data used in the description of the diffusion pattern is the percent of potential adopters who have adopted artificial insem ination. In particular, by adoption is meant the year in which a farmer became a member of the artificial insemina tion association. The data is available in aggregate form, indicating the number of new adopters in each town and commune for each year from 1944 to 1964.^ This data is only available for 46 of the 67 communes, towns and cities in Malroohus Lan. Sixteen communes are not considered in the analysis, since they were not supplied with the innovation by the Southwest Skane Artificial Insemination Association, but by agencies established in other regions. Five more communes were eliminated from the data set because of the paucity of data available, and these too are located near the 2 periphery of the region. In computing the percent of potential adopters who 1 This was collected by Dr. L.A. Brown from the records of the artificial insemination association during 1964. 2 • The sixteen units are Billesholm, Bjuvo, Brunnby, Ekeby, Halsinborg, Herrestad, Jonstorp, Kattarp, Ljunits, Morarp, Odakra, Rydsgard, Skurup, Vasby, Vemraenhog and Ystad. The latter five units are Blentarp, Klagstorp, Landskrona, Skanor med Falsterbo and Vallakra. Figure (8) indicates the location of all these communes. adopted in any given year and commune, it was necessary to obtain an estimate of the number of potential adopters. The best one available is the number of farmers enumer ated in each commune for the 1960 census (Folkrakningen, 1960). Unfortunately, we must make two assumptions; first, that the number of farmers did not significantly change through the time period under consideration, and, second, that the total number of farmers does indeed reflect the total number of potential adopters. With the available data, it is not possible to evaluate the extent to which we may be violating these assumptions. It is felt, however, that under the circumstances, the best estimate that can be made does not bias the results of the subsequent analysis to a degree which renders them bereft of utility. The Diffusion of Artificial Insemination: The Supply Perspective. As was pointed out in the previous chapter, the location of the artificial Insemination diffusion agency in Kavlinge can be considered a problem of diffu sion at the macro scale. Kavlinge was one of several regional centers chosen. The precise reasons for this choice are unknown, although some have been postulated for the relocation of the agency in Lund. The spread of artificial insemination through Southwest Skane, however, depended upon the diffusion strategies of the agency. In particular, this involved the supply and location of the public good, namely the veterinarians. The clearest Indication of the time at which a veterinarian was established is the earliest time of adoption by a farmer in a given commune. Figure (12) shows the distribution of the initial time of adoption. The first point to be made about this initial time, is that the public good was supplied to approxi mately two-thirds of the communes in the year in which diffusion first began. Twenty-nine were supplied in 1944, 2 in 1945, 12 in 1946, 1 in 1947 and 2 in 1948. All communes in the study area therefore had the innova tion made available to them within four years of the establishment of the diffusion agency. In 1944, the communes that were supplied covered a widespread area, but are most noticeably concentrated around Kavlinge and to the east. In the following year, 1945, the service was made available to two more communes, both adjacent to the former distribution. In 1946, the service was made available to a larger number of communes, the majority of which are clustered in the southwest of the region. In 1947 and 1948, the three remaining communes were provided, these being essentially peripheral to the remainder of the region. These distributions are suggestive of a number of factors in the diffusion strategy of the diffusion agency. First, there is an evident distance decay trend 50 1944 194 7 1945 and 1948 K Kavlinge L Lund I! v.v;-:-:v:*;*;*; ■;v>v>Xv>^ .v.v. ;,w>5; FIGURE 12: THE DISTRIBUTION OF THE INITIAL TIME OF ADOPTION in the initial time of adoption, suggesting that distri bution and servicing costs may have been taken into account. Second, the supply to the southwest in 1946 together with that to Ostra Fars was undoubtedly in response to the agreements between the agency and the farmers in those regions, a point made in Chapter 3. Third, the overwhelming supply in the first year of the agency's existence suggests the existence of a prior demand for artificial insemination which the agency planned to meet upon its inception. It is quite likely that for such an innovation as artificial insemination, a demand already existed within the region, particularly since many farmers were members of established bull societies. Indeed, it is even feasible to postulate that the timing of the location of the agency in the region, the macro problem, may have been dependent upon this demand. An alternative means of identifying the initial time of adoption in a commune is to estimate the intercept parameter of a linearized logistic function. The logis tic is commonly used to represent the relationship between the cumulative percent of new adopters and time of adoption, O a relationship which is often S shaped. Figures (13) to (24) show the relationship between the cumulative percent JSee Brown, 1968, for a general discussion of this function, and Jones, 1966 and Rogers, 1971 for examples of its use. 52 00 cr FIGURE 13: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (1-4) (SEE APPENDIX 1) 53 5 7 FIGURE 14: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (5-8) 54 10 11 12 » # FIGURE 15: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (9-12) 55 13 15 16 FIGURE 16: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (13-16) FIGURE 17: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (17-20) 57 21 22 23 24 FIGURE 18: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (21-24) 58 25 26 28 FIGURE 19: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (25-28) 59 29 30 31 32 FIGURE 20: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (29-32) 60 33 34 35 36 FIGURE 21: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (33-36) 61 37 38 39 40 FIGURE 22: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (37-40) 62 41 42 43 44 FIGURE 23: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (41-44) 63 45 46 FIGURE 24: THE RELATIONSHIP BETWEEN PERCENT ADOPTERS AND TIME (45-46) 64 of new adopters of artificial insemination and time of adoption for each of the 46 communes. The logistic is defined as follows A^“ A^t) 53 K/l + exp (a - bt) (14) which, when linearized, becomes In (K - A^ (t)/A^ (t)) * a - bt (15) Where A^ is the cumulative percent of new adopters in commune i, t is time, K is the celling value, taken to be equal to one, and a and b are parameters. a positions the logistic on the time axis, and b represents the rate of adoption. The data was fitted to equation (15) and the parameters estimated by least squares. The full equations, together with R values and significance tests are presented in Appendix 1. The spatial distribution of a values is shown in Figure (25) . The distribution is broadly similar to that of the actual initial times of adoption presented in Figure (12). Largest values are found in those communes furthest from the agency's headquarters at Kavlinge and from the southwest. Deviations in the estimated parameters from the actual initial time of adoption which are evi dent in some communes, are due to variations in the suitability of the logistic function in representing this relationship. 65 o values (•>v,v v.v, FIGURE 25: THE DISTRIBUTION OF a VALUES 66 The Diffusion of Artificial Insemination: the Demand Perspective. The actual adoption of artificial insemination by the farmers in each commune was obviously constrained by the supply strategies of the agency. The situation was complex, however, since the date at which the service was first supplied does not necessarily guarantee that it was supplied throughout the entire commune. Adoption, therefore, may have also depended upon this extra supply, for which data on its timing is not available. The spatial distributions of the cumulative percent of adopters are strikingly consistent from year to year. Figures (26) to (36) show these distributions for even numbered years from 1944 to 1964. Two clusters of high values are maintained around Kavlinge and in the south west. Values appear to diminish in a distance decay fashion from these centers toward the periphery of the region. A simpler means of identifying variations in the rate of individual adoption within each commune, is to view Figures (13) to (24), which show the time distri butions of adoption. There is evidently considerable variation in the rate. The spatial distribution of the estimated b parameter of the logistic function, which represents this rate, is shown in Figure (37). Those communes in which adoption was most rapid are concentrated to the east of the agency at Kavlinge and 67 Percent of adopters 1.-20 4 1 - 6 0 2 - 4 0 FIGURE 26: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1944) 68 FIGURE 27: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1946) 69 FIGURE 28: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1948) 70 FIGURE 29: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1950) 71 v. v , FIGURE 30: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1952) 72 p#.\ V . FIGURE 31: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1954) I 73 FIGURE 32: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1956) 74 . V . V v V r V . FIGURE 33: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1958) 75 FIGURE 34: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1960) 76 vMvivXm m FIGURE 35 THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1962) 77 PsSS™ X*t*XvW m m FIGURE 36: THE DISTRIBUTION OF ADOPTERS IN COMMUNES (1964) 78 v q lues 0.9 2.0 - 2 9 20 Km FIGURE 37: THE DISTRIBUTION OF h VALUES 79 Lund, and in a smaller concentration to the south. Those in which adoption was slowest are clustered around the city of Malrao and town of Trelleborg. The remaining communes are identified by intermediate rates. Although this pattern is suggestive of a regional effect on the rate of adoption by farmers, it is not clear yet which regional factors are having an influence. One of the aims of the succeeding chapter is to identify these. Conclusions. The distinctive spatial pattern of adoption of artificial insemination points to certain regularities in the diffusion of the innovation both at the meso and micro scales. Whether or not these correlate with various supply or demand factors will be established in Chapter 5. A final question that may be asked here, however, is whether the real distribution of adopters in any way conforms to the theoretical distributions outlined in Chapter 2. It was suggested there that given strict assumptions concerning the behavior of agency and poten- » tial adopters, one should expect a uniform distribution of adopters with distance from the agency. With the expansion of the public good outward and in stages, one would then expect a decreasing stepped function of distance. The relationship between the cumulative percent of adopters in each commune and distance of the commune to the agency in Kavlinge is shown graphically in Figure (38) 80 «o 1944 1948 7o' 4o £e, ¥1 Z Q. < o' /•< o • I " ‘I I "i” >'‘r 1958 1953 K Southwest communes • Others FIGURE 38: THE RELATIONSHIP BETWEEN THE PERCENT OF ADOPTERS AND DISTANCE TO KAVLINGE for four sample time periods. It Is clear that such a stepped function is not very evident in the graphs, However, due to the fact that the public good was not provided in a simple distance decay fashion, one should not expect such a stepped function. Rather, the distri bution of adopters should be a uniform function of distance only for those communes which were supplied at the same time. If the data were suitably disaggregated on this basis, a number of uniform distributions should be evident in each graph. A preliminary study of these distributions indicate, however, that they no more evidence such uniform distributions as does the total sample. Three reasons may explain why this is so. First, the time units used may not be suitably disaggregated to indicate variations in the supply of the public good. Second, initial adoption in a commune may not fully indicate the extent of the supply of the public good in a commune. Three, there may be considerable variations in the demand for the innovation amongst potential adopters. This latter problem, together with the spatial distri bution of adopters, will be tackled in the next chapter, in which a number of mathematical models are estimated. One factor which has been made clear in the descrip tive evidence of the adoption of artificial insemination, is the considerable demand in the southwest of the region. 82 Throughout most of the time period under consideration, the communes in this area had a greater percent of adopters than in allN the other communes with the excep tion of those in the immediate vicinity of Kavlinge. In Figure (38), these southwestern communes are identified 4 by an alternative symbol. It is evident that were it not for this group, a linear decreasing function of distance might adequately represent the data. There may be one or two reasons for the greater adoption in this area. The first is that not only were most of the communes supplied at the same time, but that there were also a number of special demand factors associated with the area. The second is that the communes were supplied from a subsidiary agency. It is speculated that this was located in Trelleborg. These factors would account for the early initial time of adoption in the area, which was met with a responsive demand. ^These communes are Alstad, Bara, Bunkeflo, Gislov, Nanstorp, Rang, Skegrie, Svedala, Vellinge and Oxie. CHAPTER 5 MODELS OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH SOUTHWEST SKANE; AN AGGREGATE DATA ANALYSIS In Chapter 4, evidence was provided of spatial regularities in the diffusion of artificial insemination at both the meso and micro scales. After examining the data that will be used, the present chapter reports on an attempt to model the distribution of adopters with which to compare with the theoretical outlined in Chapter 2. Second, those factors which are significantly associa ted with the strategy of the agency are identified, and, third and last, those factors associated with the demand for the innovation are identified. The Data. The origin and computation of the percent of poten tial adopters who have adopted in each commune was dis cussed in the previous chapter. For our present purposes, this data is used in modeling the spatial distribution of adop ters. Explanatory factors for the latter parts of this analysis are derived from the 1951 agricultural census and 1960 population census (Jordbruksrakningen, 1951; Folkrakningen, 1960). For each variable, the data is 83 84 available on the basis of a commune. The following variables were obtained from the agricultural census; number of bulls, number of cows, number of farm holdings and number of holdings by size class (in particular, 2-5 hectares, 5-10, 10-15, 15-20, 20-30, 30-50 and greater than 50 hectares). The following were obtained from the population census; area of the commune in hectares, number of farmers and number of farm workers. Meso Scale: The Distribution of Adopters. Under the behavioral assumptions for agency and potential adopters given in Chapter 2, the distribution of adopters should conform to the functional form stated in equation (10). A particular function of this type might be, for example, A = 5 a + bs (0 s <. s f)(H > 0) (16) I 0 (a1 < s) (H < 0) Where A is the percent of potential adopters who have adopted in a commune, s is the distance of the commune to the agency, s' is the distance at which R', economic rent after adoption, is equal to zero, and a and b are parameters. Note that the following are assumed to hold; that dA/ds “ b = 0, and that a = a(H), where H is the change in net profit after adoption. Over time, the adopter surface will rise. This may be incorporated in equation (16) by using Casetti's 85 expansion method (Casetti, 1972). Assume that a and b are functions of time. For example, 2 a = 3q + a^t + a2t . b “ bg + b^t + l>2t^ where t is time. Substituting these back into equation (16) we obtain o 2 A = aQ + a^t + + ^os + ^lsC + ^2st Where we assume that 3A/3s =* 0 3A/3t > 0 2 3 A/3s3t =* 0. Over time and given that the public good is provided in stages, a function of the form shown in equation (11) would be hypothesized. It is evident that such a function would not be continuous over the entire range of s. One means of bypassing this problem is to assume continuity and thereby derive a model of the distribution of adopters throughout the entire range (0 < s < s') and time span, and where > 0 , We must assume that the following hold, 3A/3s < 0 3A/3t > 0 . A model which satisfies these conditions Is now derived. Let A ■ exp(a - bs) (18) Using the expansion method again, we obtain a 86 space-time model A = exp(aQ + ajt + a2t2 + bQs + bjst + b2st2) (19) If during the time period under consideration the public good has been supplied only in proximity to the agency, there providing a positive incentive for adoption, and that operating costs beyond this are very high, then we expect that 32A/3s3t < 0 If, on the other hand, the public good has only been supplied toward the periphery of the region during the time period, with subsequent adoption, then we expect that 32A/3s3t > 0 If both have taken place, i.e. the supply and sub sequent demand have progressed outward, then we expect that 3 A/3s3t > 0 over the range of t. If there is reason to hypothesize the existence of more than one agency from which the public good was supplied, equations (18) and (19) may be generalized accordingly. Likewise, the above conditions apply to each agency (see Casetti, et.al., 1971; Odland, 1972; Odland, et.al., 1973 for a discussion of the testing of hypotheses in a multi-center context). In our empirical problem of the diffusion of artificial insemination, diffusion is assumed to have originated from three agencies, those of Lund, Kavlinge 87 and Trelleborg. Equation (18) now becomes A » exp (a + bs^ + cs^ + ds^) (0 (0 <. sR i s^) (0 <. sT s^) Where is the distance of the commune from Lund, sK is the distance from Kavlinge, and s,j, is the distance from Trelleborg Given that the adopter surface changes over time with respect to each agency, we obtain by expansion, A = exp(aQ + a^t + a2t2 + ^0SL + + ^2sLc2 + C0SK 2 9 + c^s^t + CjS^-t + dgST + d-^sTt + d2S^ft) (21) and in which the following are hypothesized, 3A/3t > 0, 3A/3sl < 0, 8A/3sk < 0, 3A/3st < 0 Conditions similar to those for equation (19) will also hold in equation (21) with respect to each agency. In other words, if adoption occurs largely in the vicin ity of any agency, then 32A/3sL3t < 0, 32A/3sK3t < 0, 32A/3sT3t < 0 or if it occurs further from the agency, 32A/3sL t > 0, 32A/3sK3t > 0, 32A/3sT3t > 0 or if it occurs at first in close proximity and later farther out, then 32A/3sL3t $ 0, 32A/3sK3t £ 0, 32A/3sT3t $ 0 An Empirical Test. The parameters of equation (21) were estimated by least squares, after linearization and using data on the adoption of artificial insemination from 1944 88 to 1964 for the 46 communes. The resulting equation and R.2 value, showing only those parameters that are signi ficantly different from zero using the ’t' test, are as follows, R2 = .70 A - exp (-1.6 + 0,34t - 0.013t2 + 0.015s - 0.078s,. (9 .42) (7 .97) (3.04) (10.877 (22) + 0.0059s„t - 0.00017 s„t2 - 0.028s,,, + 0.000039sTt2) (4.52) K (2.99) K (12.19? (4.22) T On the basis of the F ratio, the correlation coeffi cient is significantly different from zero at the 1% level. Student's 't' values, shown in parentheses, also indicate that the estimated parameters are significantly different from zero at the 1% level. As expected, the distribution of adopters is a decreasing function of distance to both Kavlinge and Trelleborg. The fact that SA/Ss^ is equal to 0.015 and is significantly positive, perhaps reflects the fact that Lund is located between the previously established agencies. Since 32A/3sj,3t > 0 and 32A/3sT 3t > 0, we can assume that over the given time period the supply and adoption of artificial insemination was predominant at distances further from these agencies at Kavlinge and Trelleborg. This does not imply that those areas closer to the two were not supplied and that there was no subsequent adoption. The fact that 3A/3s,. and 3A/3s are both K. T significantly less than zero shows that they were. Rather, 89 it indicates that these were supplied at a fast rate at the beginning of the time period, with considerable adoption. This bears out the evidence presented in Chapter 4. Meso Scale: The Diffusion Strategy. In the theoretical framework presented in Chapter 2, it was argued that the meso scale problem was one of supplying the public good to various locations. A theo retical strategy on the part of the agency and the resulting distribution of adopters was outlined and modeled. This was tested In the previous chapter, and it concluded that the public good was supplied in stages with distance from the agencies. A number of alternative factors important in this strategy were also put forward. Here we will test their significance. It must be pointed out, however, that to a large extent we are at the mercy of the avail able data. Assuming that the provision of the public good is in response to its expected profitability, the latter will be a function of a number of benefit and cost factors. Moreover, the supply of the public good will also be guided by a prior demand, one that existed before and perhaps resulted in the location of the agency. We therefore hypothesize the following. The date at which the artificial insemination service is supplied to a commune is 90 (1) negatively related to the expected benefits associated with that commune. This will be represented by the number of farm- % holdings (X^) ,which is a surrogate for expected returns, (2) positively related to the costs associated with supplying and maintaining the service. These will be represented by the density of farmers (X ) and the distance from the 2 commune to each of the three agencies, Kavlinge (Xg), Lund (X^) and Trelleborg (Xg) , (3) negatively related to the prior demand for the service. This is represented by the percent of farm-holdings in a commune greater than 30 hectares (X^), the average number of bulls owned by each farmer (X^) and the average number of cows (Xg). An Empirical Test. The Intercept, a, of the linearized logistic function, which was estimated for each commune is used as an index of the date at which a commune was first supplied by an agency.^ The specific model, the parameters of which are to be estimated is as follows, 8 a = a(Xx,X2,..., X8) = c + <23> ^The logistic was defined as equation (15) in Chapter 4. The estimated parameters are given in Appendix 1. 91 where c and d. through d are parameters, and the x 8 following are hypothesized, for hypothesis (1); 3a/3X^ < 0 for hypothesis (2); 3a/3X. > 0, 3a/3X_ > 0, 3a/3X_ > 0, o t o 3a/3X2 < 0 for hypothesis (3); 3a/3X^ < 0» 3a/3X^ < 0, 3a/3X^ < 0. The parameters of equation (23) were estimated by least squares. Only those that are significantly dif ferent from zero using the t test as the criterion are 2 reproduced. The estimated equation, R value, F ratio, 't' values and standardized regression coefficients ($) are as follows, R2 = .74 (F3 38 = 15.75) a - 1.51 - 0.0048X. - 2.52X, - 3.02X + 0.049X. + 0.035Xft (24) (2.89) (2.25? (2.08? (2.31)6 (3.12)° (8) -0.78 -0.28 -0.45 0.63 0.62 The correlation coefficient is significantly differ ent from zero based upon the F ratio at the 1% level, and those parameters shown are significantly different from zero using the 't' statistic at the 5% level. These results provide a reasonable, though not conclusive, confirmation of each of the hypotheses. Given the acceptability of the definition of the variables, the supply strategy does appear to be a function of expected benefits and costs and of prior demand. The 0 coefficients indicate that the number of farm-holdings in a commune 92 had the greatest impact on the supply date. One final remark should be made concerning this model, and that is that we have not been able to allow for the existence of perceptual biases on the part of the agencies' decision-makers. If such biases exist, the most satisfactory means of establishing them is through the use of questions concerning the similarity of potential supply locations. Through such data, the structural dimensions of each decision-maker's perceived space may be obtained. Although this was not possible in this study, it would be of considerable value In any such further ones. The spatial distribution of the residuals from equation (24) is shown in Figure (39). There does not appear to be a consistent trend for those communes in which the date of the availability of the innovation was predicted too early. Those which were predicted later than their actual initial time of adoption, seem to be concentrated near to the agency in Kavlinge and in the southwest. These distributions are not particularly striking, and are not immediately suggestive of other factors that should be included in the model. The Micro Scale: Demand and Adoption. It was argued in Chapter 2, that the micro scale problem of diffusion is demand oriented. The components of the individual adoption decision and those factors 93 v.y, £«** Xv«v«*« y.v/.y VvV.V>*V*V|VA X'»W*XW*1* FIGURE 39: THE DISTRIBUTION OF RESIDUALS FROM EQUATION (24) 94 which may be influential in that decision were discussed. Variations in the rate of adoption amongst communes are assumed to reflect variations in the decision processes, and its influential factors, of individual potential adopters, The availability of information, both at the awareness and search stages, is one important factor in the deci sion to adopt. A second are the goals, aspirations and motivation of the potential adopters. These will be reflected in such personal characteristics as age, education, income, status, business size, specialization and the like. A third is the expected utility or profit ability of adopting the innovation. A major cost asso ciated with adoption are the operating costs of the public good or artificial insemination service. It will be assumed that if the service is available costs are generally low, and if it is not, then costs are infin itely large. In reality, the rate of adoption may be slow due to the fact that the commune has been ineffec tively supplied. Regretably the data needed to confirm this is not available. There are two major benefits resulting from the adoption of artificial insemination. First, assuming the innovation to be capital and labor saving, there will be a reduction in production costs. This might be par ticularly true if the prices of these inputs are high. 95 Second, and this factor is more peculiar to artificial insemination, there are long-term benefits associated with the improved quality of the herd. This particular factor is often used as a selling point in the diffusion of artificial insemination. Such benefits may be greater to farmers with larger herds. Perhaps more importantly, the rate of adoption may be greater in those areas where farmers have the ability to gauge these long-term benefits. We therefore hypothesize the following; the rate of adoption of artificial insemination in a commune is (1) positively related to the amount of infor mation that is available concerning the innovation. This is represented by the density of farmers (X£) and distance to each agency (X^, X^ and Xg), (2) positively related to the size of business or farm operation. This is represented by the percent of farm-holdings greater than 30 hectares (Xg) and the average number of cows owned by farmers (X^), (3) positively related to the expected profit ability of innovation. This is represented by the average number of bulls owned by farmers (X^) and the average number of farm workers per farmer (X^). It is apparent that most of the variables in this 96 analysis are the same as those in the previous one, although they have been, given different interpretations. In the analysis of the diffusion strategy of the agency, the aim was to identify those factors, as perceived by the agency, that were significantly associated with that strategy. In analyzing the diffusion amongst the indi vidual farmers, the aim is to identify those factors relevant to these that explain variations in the rate of adoption. The variables used will therefore differ only in the interpretation of their significance in explaining these two phenomena. An Empirical Test. The parameter, b, of the logistic function was used as an index of the rate of adoption in a commune » The specific model is as follows* b = b(X2 , X3 , ..., X9) - f + I giXi (25) Where f and g2 through gg are parameters, and the fol lowing are hypothesized, for hypothesis (1); 9b/9X2 > 0, 9b/9Xg' < 0, 9b/9Xy < 0, 9b/9Xg < 0 for hypothesis (2); 9b/9X^ > 0> 9b/9X^ > 0 for hypothesis (3); 9b/9X^ > 0, 9b/9Xg > 0. The parameters of equation (25) were estimated by least squares. The estimated equation, R value, F ratio and 11 ’ value are as follows, 2 See note 1 in this chapter. 97 R2 « .44 (Fx 4A = 34.66) b - 0.228 - 0.0658X. (26) (5.89) Quite obviously equation (25) is a fairly inadequate model of the rate of adoption, even though the correla tion coefficient and parameter are significantly different from zero at the 1% level. Given the variables used, the rate of adoption by farmers in a commune does not appear to be related to information availability or to farm size. Moreover, 3b/3Xg appears to have the wrong sign. The estimated model suggests that the rate of adoption is greater in communes where the average number of farm workers per farmer is less. It could be argued, however, that this is not contrary to the hypothesis. The reason is two-fold. First, a low average may reflect ' the fact that the price of labor is high or the supply low and, second, since the data on farmers and farm workers is derived from the 1960 census, towards the end of the time period under consideration, this may actually reflect a decrease in the average as a result of rapid adoption. The distribution of residuals from equation (26) is shown in Figure (40) . There does not appear to be a consistent spatial trend for either those communes for which the rate of adoption was overpredicted or for those for which the rate was underpredicted. 98 20 Km FIGURE 40: THE DISTRIBUTION OF RESIDUALS FROM EQUATION (26) 99 Conclusions. In this chapter, we have presented an analytic approach to explain the spatial regularities of the diffusion of artificial Insemination in terms of the theory outlined in Chapter 2. A simple model of the distribution of adopters with respect to a set of agencies was derived and parameters estimated with the use of the aggregate adoption data. Second, a set of hypotheses concerning the supply strategy of the agencies were tested. The hypotheses were confirmed, and the model provided a reasonable explanation, in terms of variance accounted for, of supply time. A similar model used to test hypotheses concerning the demand for the innovation or the adoption rate was relatively unsuc cessful. The hypotheses were rejected and the explana tory power of the model low. It appears that one of the major reasons for this failure is due to the aggregate nature and paucity of data. This will be rectified In the succeeding two chapters, which present an analysis of the interface between raeso and micro scales, using data for a sample of individual adopting farmers. CHAPTER 6 DESCRIPTIVE PROPERTIES OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH A SAMPLE OF FARMERS: AN INDIVIDUAL DATA ANALYSIS The empirical analysis of the diffusion of artificial insemination has thus far relied upon the use of aggre gate data. Chapters 6 and 7 present analyses that use data on the adopting behavior of individual farmers. Such data is more suitable for the testing of hypotheses concerning the decisions giving rise to diffusion. In the present chapter, this is accomplished by describing the course of diffusion through a sample of farmers. The Data. The sample consists of 562 farmers in the vicinity of Horby^, The area from which the sample is taken is shown in Figure (41), whilst Figure (42) provides a detailed map of the specific area. The northern part of the region is composed of most of the commune Ostra Frosta. The parishes in this commune are, from north to south, Sodra Rorum, Fulltofta, Aspinge, Horby and Lyby. To the east is the parish of > ^This data was obtained by Dr. L.A. Brown in 1964 from the records of the Lydvastra Skanes Semin- forening. 100 101 FIGURE 41: THE LOCATION OF THE SAMPLE AREA 102 A-; Lyby lerup FIGURE 42: THE SAMPLE AREA IN DETAIL 103 Ostra Sallerup in the commune Langarod. To the west is a small portion of the commune Snogerod, and to the south west the parish of Hogserod in the commune Loberod. Finally, to the south are the parishes of Vasterstad and Ostraby in the commune Bjarsjolagard. The locations of the adopters are shown in Figures (43) to (61) for each of the years from 1946 to 1964. The former is the first year of adoption in the area according to this sample. The Pattern of Diffusion. In 1946, the first farmers adopted artificial insemination in Vasterstad and western Ostraby (see Figure (43)). In the following year, diffusion continued within the same two areas (Figure (44)). In 1948 (Figure (45)), the innovation diffused to Hogserod to the west, to southern Lyby and to western Ostra Sallerup. In 1949 It moved Into the northern portion of Snogerod, western Lyby and to eastern Ostraby (Figure (46)). The following year witnessed a further westward movement in Snogerod (Figure (47)). From 1951 to 1953, the innovation moved rapidly northward. In 1951 (Figure (48)), it moved to northern Lyby and in 1952 (Figure (49)) to Horby. By the year 1953 (Figure (50)), farmers had adopted the innovation in western and eastern Horby, eastern Ostra Sallerup and in the parishes of Fulltofta, Sodra Rorura and Aspinge. I 104 on Adopters • Adopters •o FIGURE 43: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1946) 105 t & FIGURE 44: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1947) 106 A-J ^•• *• \u* * • w • • FIGURE 45: THE DISTRIBUTION OF INDiviDUAL ADOPTERS (1948) 107 FIGURE 46: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1949) 108 A-: \*-J •* * • • • * • *- FIGURE 47: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1950) 109 •• «.• FIGURE 48: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1951) 110 FICORE 49: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1952) Ill — n__» • • • * i >. / W o© FIGURE 50: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS- (1953) 112 f * FIGURE 51: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1954) 113 FIGURE 52: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1955) 114 FIGURE 53: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1956) 115 FIGURE 54: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1957) 116 * r FIGURE 55: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1958) 117 FIGURE 56: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1959) 118 FIGURE 57: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1960) 119 FIGURE 58: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1961) 120 • • >*• • • * » FIGURE 59: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1962) 121 FIGURE 60: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1963) 122 FIGURE 61: THE DISTRIBUTION OF INDIVIDUAL ADOPTERS (1964) Throughout the time period from 1946 to 1953 although the innovation had moved from one parish to another, diffusion within each area was maintained. From 1954 to 1964 (Figures (51) to (61)) diffusion occurred largely in those areas in which there had been previous adoption. An Interpretation of the Diffusion Pattern. Figures (43) to (61) are strongly suggestive of two phases in the diffusion of artificial insemination. From 1946 to 1953, the innovation spread from the south to the periphery of the region to the west, north and east. It may be hypothesized that this spread reflects the availability of the innovation to the potential adopters. In parti cular, this would respresent the supply of the service by the agency, in the form of veterinarians. Once the innovation becomes available, individual adoption and diffusion continues within that area. It should also be noted that the area in which adoption first occurred, in 1946, is closest to Lund, the location of the Sydvastra Skanes Seminforening. A second phase, from 1954 to 1964 is apparent. Adoption does not spread outwards, since it had already reached the periphery. Rather, it occurs in areas in which the Innovation seemed to be already available. This would suggest that diffusion during this phase was largely a result of Individual adoption behavior. It is possible, however, that the innovation was still being 124 made available to potential adopters in some parts of the region. It could be argued that the reason for the diffusion of artificial insemination through the region in the first i phase, is to be found in the interpersonal spread of information regarding the innovation. This argument follows the more traditional explanation of diffusion (Hagerstrand, 1952, for example). It really seems doubt ful, however, that it could have taken as long as eight years for the information to have spread fourteen miles from the south to the north of the region, and this in a developed rural society. This, then, reinforces the hypothesis that this spread was due to the innovation being made available by the agency to potential adopters at certain times. Conclusions. The data presented in this chapter provides tenta tive evidence for the Importance of both the supply and demand related aspects of diffusion. Models of diffusion, involving both of these, are presented and tested in the next chapter. CHAPTER 7 MODELS OF THE DIFFUSION OF ARTIFICIAL INSEMINATION THROUGH A SAMPLE OF FARMERS: AN INDIVIDUAL DATA ANALYSIS Models of the time of adoption will now be tested, using data for the sample of farmers near Horby. The models are derived within the theoretical framework provided in Chapter 2, and are based both on the supply and demand related aspects of diffusion. In particular, the first model Is a single linear equation and the second a 'causal model'. The Data Apart from the time of adoption of each individual in the sample, which is used as a dependent variable, a number of other variables are used as explanatory factors. The data set is divided into two. One is available for a sample of 562 farmers and consists of the following; the farm acreage, the number of cows owned by the farmer,^ the density of farmers in each farmer's neighborhood, where this is defined as being within a radius of one ■^These two variables were obtained form the 1960 population census. 125 126 kilometer from the individual, the time at which the first farmer in each farmer's neighborhood adopted artificial insemination, and the distance from each farmer to Kavlinge, Lund and to a predetermined point to 2 the south of the region. The second set is available for a sample of 178 farmers and consists of the following; those variables in the first set, together with the income derived from agriculture, the age of the farmer, the number of rooms in each farmer's house, whether the farmer possesses a car, central heating, warm water, a refrigerator, a 3 stove, a bath and an Inside toilet and finally, the number 4 of acquaintances that each farmer has. A Model of the Time of Adoption The variables outlined above are used in a model of the time of adoption in order to test a set of hypotheses generated from the theoretical framework. The density of farmers in an individual's neighborhood (Y^) is assumed to represent the profitability of supplying the innovation to that neighborhood. The distances from Kavlinge, Lund 2 These five variables were computed from a map of the location of each farmer, 3 These variables were obtained from the 1960 popu lation census, population register and Income register. ^This variable was derived from each respondent to a questionnaire. See Appendix 2. 127 and a point south (Y , Y and Y ) represent service costs 2 3 4 to the agency in supplying.the innovation. The latter variable is computed since it has been shown in Chapter 4, that the adoption and supply of artificial insemina tion was, at first, greater to the south of the region. The innovation later diffused from the south to the north and east. The time at which the first farmer in the neighborhood adopted (Y^) is assumed to represent the time at which the innovation was first supplied to that area. The farm size (Y^) represents the social status of the individual, and the size of his herd (Y ) 6 represents the extent to which the innovation is pertin ent to the farmer. Agricultural income (Yg) and the number of rooms (Y^) are alternative measures of social status. The number of acquaintances (Y^) represents the potential of the farmer for receiving information concerning the innovation. An index was computed to represent the innovativeness of each farmer (Y^^). This consists of the summation of the possessions of each individual, namely car, central heating, warm water, refrigerator, stove, bath and inside toilet. A final variable is the age of the farmer (Yj^). It is suggested that younger farmers are more likely to consider the essentially long term benefits of artificial insemination for their herd. Within the context of the theoretical framework, the following are hypothesized; that the time at which 128 a farmer adopts artificial insemination is (1) negatively related to the profitability of supplying the Innovation (Y^), (2) positively related to the service costs asso ciated with the innovation (Y_, Y_ , Y,), 2 3 4 (3) positively related to the time at which the Innovation was supplied to the neighborhood (Y^), (4) negatively related to the social status of the farmer (Y?, Yg, Yg) , (5) negatively related to the relevance of the innovation (Yg), (6) negatively related to the farmer's potential for receiving information (Y^q)* (7) negatively related to the farmer's innovativeness (8) positively related to the age of the farmer (Y^2), The following model is used to test the above hypotheses, 12 T = T ^ , Y2, . .., Y12) o a + £ b±Yi (27) Where T is the time of adoption and a and b^ are parameters. Equation (27) was estimated for both the large and small samples, with only variables Y^ through Y^ being estimated for the former. The Results for the Large Sample. The parameters of equation (27), using variables Y^ through Y^, were 129 estimated by least squares. The resulting equation, with only those parameters significantly different from zero 2 shown, together with the R value and F and 't* statis tics are as follows R2 » .24 T » 989.12 + 0.497Y5 - 0.238Yfi (28) (9.88) (8.19) Although the correlation coefficient is significantly different from zero, the variance accounted for by the model is low. The result suggests that the time of adoption is positively related to the supply time and negatively related to the relevance of the innovation, as represented by the size of the herd. The spatial distribution of the larger positive and negative residuals (see Figure (62)) does not in itself suggest the existence of alternative explanatory factors. An examination of the residuals does indicate, however, that the earlier adopters were consistently overpredicted, whereas later adopters were consistently underpredicted. This suggests that the variables in the model should be transformed in order to adhere to the assumptions of the linear model. The Results for the Small Sample. Equation (27) was fitted to the data representing the small sample for two reasons. First, a larger number of the hypotheses could be tested, and second, it was considered that measurement 130 FIGURE 62: RESIDUALS FROM EQUATION (28) error would be reduced In this subsample, since it was obtained from the central portion of the region. The parameters of equation (27) were therefore estimated by least squares. The resulting equation is as follows RZ = .39 (F^ (174 “ 36.36) T = 758.68 + 0.615Y _ - 0.124Yfi - 0.00011Y_ (29) (9.06)D (2.40) (2.30) 8 These results suggest that the explanatory power of the model has Increased and that hypothesis (4) is confirmed, i.e. that the time of adoption is negatively related to social status. Following the results in equation (28), 3T/3Y^ > 0 and 3T/3Yg < 0. Also, as in the case of the larger sample, the residuals indicate that earlier adopters were consistently overpredicted and later ones underpredicted. The residuals from equation (29) are shown in Figure (63). The results of the models in this section illustrate at least three problems. First, they provide a fairly low level of explanatory power. Second, there is some doubt as to whether the variables are capable of being used to test the hypotheses. Third, it is evident that C JThe hypotheses were also tested in an alternative manner. Factor analysis was employed to uncover the structural dimensions in the variable space. Two factors, termed innovativeness and social status, were signifi cantly related to the time of adoption in a regression model, with an RZ value of .38. With innovativeness defined this way, therefore, hypothesis (7) can not be rejected. Appendix 3 provides details of this analysis. 132 o • FIGURE 63: RESIDUALS FROM EQUATION (29) 133 the model is representing a two-stage process, the first concerned with the supply of the innovation and the second concerned with individual adoption. Moreover, many of the variables are causally dependent and not inde pendent, as is the assumption of the regression model. One means of tackling this latter problem is considered next, A Causal Model of the Time of Adoption. Based on the two-stage nature of the diffusion process, the model presented in Figure (64) is suggested. Availability of the innovation (Y^) depends upon the supply strategy of the agency. This is in turn a function of expected profitability and service costs (Y^and Y3). Only distance to Lund, the location of Sydvastra Skanes Seminforening, was included in order to simplify the model. The second stage, adoption by the individual, depends upon the time at which the innovation is made available (Y^) , the size of the herd (Yg) , agricultural income (Yg) , innovativeness (Y^) and potential for receiving information (Y^q) . It is also hypothesized that innovativeness is in part a function of income and that income is in part a function of the size of the herd. All the simple correlation coefficients indicated in Figure (64) are significantly different from zero according to the F ratio. Size of farm (Y7), number of rooms (Y^) and the age of the farmer (Yj^) were not 134 6 V. Y Y. '10 FIGURE 64: A CAUSAL MODEL OF THE TIME OF ADOPTION 135 entered into the model directly, since they were not significantly correlated with the time of adoption. Following Blalock (1961), this model may be evaluated by hypothesizing a set of correlation coefficients and then comparing them with the actual ones. Table (1) shows both the expected and actual coefficients for a number of relationships in the model, together with their F ratios. In order to reject the null hypothesis that r^O in each case, the F ratio must be greater than 3.89 at the 57. level or greater than 6.76 at the 1% level. As hypothesized, r^g, r^g and are not significantly different from zero. Moreover, r^T is approximately equal to rj^ r^rj, (and hence ^3 1 .5 assumed to be zero). The expected value for r g u differs substantially from the actual value, however, and this suggests that g is not equal to zero. The model is accordingly changed by adding a link between Yg, the size of the herd, and Y ^ , the farmer's innovativeness. A final comment concerns the relationship between Yi0 , the acquaintance variable, and Y^, the supply time variable. The simple correlation is significantly different from zero, but this may be due to a relationship between Y ^ and Y^, the density of farmers. The correla tion between number of acquaintances and density, r^g, is .22, which is also significantly different from zero. To test whether this relationship influences that between 136 TABLE 1 HYPOTHESIZED CORRELATIONS FROM THE CAUSAL MODEL CORRELATION EXPECTED ACTUAL F1 ,176 00 o CM 1 • r56 0 • r58 0 -.04 .28 r511 0 -.04 .28 r510 0 -.23 9.83 rlT r15r5T " “ .39 -.43 .30 r3T r35r5T = *35 r 611 r68r811 = *28 .46 137 Y^0 and Y^, the following should hold; that ^ r110 r105 and that 1^X5 .id > °* In fact rliQ r105 is equal to -.05, which is considerably less than r^5 = -.69. Also, lr15,lo| equal to .67, which is significantly greater than zero using the F ratio. The causal model may be tentatively accepted on the basis of this evaluation. A link between Yg and Y-^ can be added, and the relationship between Y^q and Y^ appears to result from the influence of Y^. The process is regarded in two stages, one concerned with supply and the other with adoption. The latter itself can be regarded as a multi-stage process, since the explanatory factors Y-j^ and Yg are dependent upon Y^, Conclusions. In this chapter we have derived and tested models of the diffusion of artificial insemination amongst a sample of farmers. Two models were used, the first a single linear equation, and the second a causal model. The latter model is considered the more suitable, since it accounts for both the multi-stage nature of the diffusion process and the interdependencies between the explanatory factors. CHAPTER 8 SUMMARY AND CONCLUSIONS A Summary. This dissertation has reported on empirical work carried out within the context of a theory of diffusion of innovation originally proposed by Brown (1973). The theoretical framework is oriented towards supply related aspects of diffusion, which is in contrast to most pre vious geographical diffusion theory, this being oriented towards the demand behavior of individuals. The present theory involves two components; the establishment and location of diffusion agencies, termed the macro scale problem, and the strategy by which such agencies reach potential adopters, termed the meso scale. The original framework has been extended, and models of the location decision for the propagator and agency and a model of the spatial distribution of adopters are derived. The major components of the decision models are the costs and benefits associated with each potential location. The models may be modified to account for perceptual biases of the marketing surface on the part of the decision makers. The model of the distribution of adopters is based upon the assumption of profit maximizing 139 behavior of the producer/potential adopter, and that the innovation is an input to an ongoing economic activity. In addition to the present theoretical framework, the decision making behavior of potential adopters is reviewed and further conceptualized. The model of the distribution of adopters is then modified to account for variations in the extent to which information concerning the innovation is available to those potential adopters. The theoretical framework was evaluated using data of the diffusion of artificial insemination of cattle amongst farmers in southwest Skane, Sweden, over a period of twenty-one years. The supply of this innovation in Skane began in 1944 with the establishment of the Kavlingeorteus Seminforening, and later of the Sydvastra Skanes Seminforening in Lund. This agency in turn supplied the innovation through veterinarians located within the region. The analysis of the diffusion of artificial insem ination was undertaken with the use of two data sets. The first, an aggregate set, is available on a commune basis for those communes in Malmohus Lan. The second, an individual set, is available for a sample of farmers in the vicinity of Horby. In the former, the spatial trends of the time at which the innovation was first supplied to farmers in a commune and the rate of adoption by potential adopters were analysed. This was accomplished 140 by describing the course of diffusion and by the use of multiple regression models. The results suggest that the hypothesized distribution of adopters based upon restrictive behavioral assumptions is not apparent in the data, although the innovation does appear to have been supplied in stages with increasing distance from the agency. More over, the time of supply in a commune is related to the benefits and costs associated with each commune. The results of the model for the rate of adoption were less satisfactory, indicating that only expected profitability of the innovation is significantly associated with this rate. The second analysis identified those factors signi ficantly associated with the time at which the innovation was supplied in the neighborhood of a farmer, together with those associated with the time of adoption by indi vidual farmers. The results indicate that the diffusion is a two step process, the first related to the supply and the second related to the demand and adoption of the innovation. The time of supply of the innovation is associated with the benefits and service costs attributed to the neighborhood. The time of adoption is associated with the time of supply in the individual's neighborhood and, to a lesser degree, the potential of the individual for receiving information, the size of the farmer's cattle herd and his social status. 141 Some Critical Comments and Notes for Further Research. The following comments are oriented toward the theoretical framework, the models and the empirical study reported in the dissertation. The Theoretical Framework. Due to the previous lack of research on the supply related aspects of diffusion and the dominance of demand aspects, especially following the work of Hagerstrand, the present theoretical framework has not been exposed to rigorous debate amongst interested researchers. The components of the decision making process for individuals on both the supply and demand sides needs to be defined, together with the ways in which these are expected to vary with differing sets of behavioral assumptions. Having defined these, expected spatial trends in diffusion may be generated. More research is also needed to identify those factors that affect the supply and adoption decisions. In part such work will be deductive, though we might expect the greater part to result from empirical work and the analysis of case studies. The Models. Models should be developed which are truly representative of the theoretical framework. To a large extent, the specification of such models will, however, depend upon the status of this framework. Models should be derived for the general and specific cases outlined in the theory. One type of model relates to the location and adoption decisions of individuals. These must account for variations in learning, perception and decision rules. The second type of model relates to the expected distri butions of adopters and spatial trends of diffusion resulting for these differences in behavior. In this dissertation we have derived only a small number of these. Finally, the very nature of the diffusion problem points to the inadequacy of the single equation model. Diffusion is a multi-stage process, and ought to be represented by a system of equations. Causal analysis is a preliminary means of identifying such a system. The Empirical Study. A great deal of empirical research is needed to evaluate and modify the various aspects of the theoretical framework. A major problem with the present study is the failure to fully test a set of hypotheses, due to the lack of suitable data. In the future, data should be collected to correspond to those variables in the models necessary to test these. Questionnaires also should be employed to Identify the perceptual and preferential biases of decision makers, so that these too may be incorporated in the models. Finally, it is felt that personal experience with the particular empirical problem, perhaps in the form of a field or case study, would enhance the researcher’s understanding of the behavioral components, strategies and Influential factors of each decision maker. This understanding would subsequently benefit the development 143 of the theoretical framework as well as its practical utility in problems of regional development. 144 APPENDIX 1 O R Values, F Ratios and Estimated Parameters of the Logistic Function for Each Commune in Malmohus Lan Commune Parameter Number Name a b R2 F1 »19 1 Alstad 3.46 -.28 .74 54.39 2 Anderslov 4.57 -.14 .54 20.26 3 Bara 1.30 -.13 .68 35.83 4 B j arsj olagard 3.63 -.21 .64 34.34 5 Bosarp 3.16 -.22 .73 50.71 6 Bunkeflo 1.50 -.07 .74 49.61 7 Burlov 2.45 -.06 .40 12.79 8 Dalby 1.98 -.18 .68 35.41 9 Dosj ebro 2.29 -.16 .83 90.68 10 Eslov 2.54 -.16 .82 88.91 11 Furulund 1.64 -.19 .84 98.68 12 Genarp 3.53 -.19 .74 53.07 13 Gislov 2.66 -.22 .63 28.42 14 Harrle 2.10 -.15 .76 61.39 15 Harslov 2 .20 -.11 .66 36.84 16 Kagerod 5.25 -.17 .61 25.39 17 Kavllnge 1.29 -.13 .93 248.46 18 Langarod 5.00 -.22 .82 85.57 19 Loberod 3.32 -.21 .71 47.50 20 Loddekopinge 2.05 -.18 .69 42.42 21 Lotnma 2.09 -.11 .68 40.84 22 Lund 2.41 -.14 .63 32.74 23 Malmo 3.00 -.06 .72 43.52 24 Manstorp 1.33 -.12 .70 40.47 25 Marieholm 2.76 -.21 .74 54.42 26 Norra Frostra 4.73 -.21 .86 115.54 27 Ostra Fars 3.86 -.13 .55 20.59 28 Ostra Frosta 4.28 -.21 .83 90.81 29 Oxie 2.32 -.14 .46 15.89 30 Rang 1.34 -.15 .65 31.44 31 Ronneberga 2.67 -.18 .67 38.20 32 Rostanga 4.14 -.19 .70 41.98 33 Sj obo 3.63 -.18 .78 67.69 34 Skarhult 3.74 -.23 .76 58.92 35 Skegrie 1.19 -.12 .56 21.62 36 Snogerod 3.55 -.21 .76 52.50 37 Sodra Sandby 3.63 -.22 .68 41.11 145 38 Staffanstorp 2.61 -.19 .67 39.36 39 Svalov 1.93 -.14 .72 49.08 40 Svedala 2.08 -.22 .89 134.05 41 Teckomatorp 1.94 -.17 .80 73.84 42 Torn 1.44 -.17 .80 74.96 43 Trelleborg 1.92 -.05 .33 7.52 44 V eberod 3.15 -.11 .69 33.20 45 Vellinge 2.68 -.23 .63 32.12 46 Vollsjo 3.55 -.20 .62 28.99 146 APPENDIX 2 The Computation of the Acquaintance Variable. Each respondent was furnished a list of names of those fellow, members of the Sydvastra Skanes Seminforening to whom a questionnaire was also sent. The respondent was asked to indicate which individuals in the list he had (1) spoken to during his year of adoption, (2) spoken to during the last few years, (3) discussed farm problems with regularly and (4) discussed farm problems with most frequently. A symmetric matrix of acquaintances was constructed, the 1/0 elements of which indicate at least a one-way acknowledgement of acquaintanceship under any of the above four criteria. Variable is the summation of the acquaintances for each respondent. This data was obtained by Dr. L.A. Brown, and the variable was computed by Aron Spector. 147 APPENDIX 3 The following material is supplementary to the main body of the text. It is divided Into three sections. The first presents three matrices of simple correlations; the second, the results of two factor analyses; the third, the results of two regression models of the time of adoption. Correlation Matrix for the Aggregate Data a b x 2 X1 X3 \ X5 X 6 X7 X8 b .45 X x ,.,.61 .39 X2 -.09 -.05 .24 X 3 -.67 -.35 -.61 -.19 X4 .26 .10 .04 -.49 .06 X c .21 .43 .28 -.57 -.03 .44 « X6 .35 .07 .38 .03 -.19 .12 .01 X, .42 .11 .42 -.04 -.32 -.09 .03 .79 X8 .47 .30 .46 -.01 -.56 -.04 .28 .04 .04 X9 -.45 -.66 -.58 .04 .47 -.14 -.48 -.10 -.22 -.48 Correlation Miatrix for the Large Individual Sample *7 Y 6 Y 1 Y5 y 2 y3 Y6 .71 Y -.12 -.11 Y5 -.03 -.07 -.58 Y, -.14 -.05 -.32 .42 Y3 -.14 -.07 -.37 .57 .97 Y, .01 -.08 -.36 .75 .12 .36 4 148 Factor Analysis of Large Sample Final Factor Communality 1 2 3 .06 -.91 -.12 .84 Y7 -.05 -.92 .02 .86 Y 6 -.65 .21 -.29 .55 Y 1 .88 .05 .32 .89 Y5 Y .12 .05 .99 .99 2 Y3 .32 .08 .93 .97 .91 .09 -.01 .83 Y4 Eigen 2.98 1.76 1.20 value Cumula- .43 .68 .85 tive % Factor Analysis of Small Sample Final * Communality Factor 1 2 3 4 .17 .01 .90 .10 .84 *7 .24 .04 .81 .27 .80 T 6 .02 -.83 -.13 .04 .71 Y1 .01 .82 .03 .10 .68 Y5 Y .08 .85 -.04 .13 .75 2 .06 .93 -.03 .07 .87 Y3 -.06 .74 -.01 .18 .59 Y4 .43 Y 10 .25 -.23 .11 .55 .56 Y 8 .45 -.01 .48 .34 149 Y 1 2 3 4 Y9 .22 .03 .76 -.02 .62 Y-. -.83 -.02 -.20 -.02 .73 (toilet) -.02 y14 "*84 -.16 .08 .73 (bath) Y15 .29 -.34 .08 -.31 .30 (central heating) .47 -.12 .18 .02 .27 (warm water) Y 12 *79 .01 .17 -.16 .68 (refrigerato r) Y18 *63 .16 .06 -.30 .52 (stove) -.05 .17 -.67 .55 *19 . 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