1996 CANADIAN CENSUS DEMOGRAPHIC VARIABLES IMPUTATION Michael Bankier, Anne-Marie Houle, Manchi Luc and Patricia Newcombe Anne-Marie Houle, Statistics Canada, Ottawa, Ontario, Canada K1A 0T6, [email protected] KEYS WORDS: Minimum change hot deck imputation, resemble that single donor. inconsistent response, couple edit rules. (c) Equally good imputation actions, based on the available donors, should have a similar chance of being 1. INTRODUCTION selected to avoid falsely inflating the size of small but important groups in the population. Among the basic questions asked of every Canadian Besides respecting these objectives, the NIM on Census Day are the five questions related to the attempts to deal more effectively with the frequent demographic variables age, sex, marital status, common- response errors that were not well resolved by the E&I law status and relationship to Person 1. The responses system used in the previous censuses. To achieve this given to these questions are examined simultaneously for objective, the new methodology was developed in parallel all persons in a household to identify missing and with the modification of the edit rules such that they now inconsistent responses and to make the appropriate reflect more accurately the changes in the Canadian corrections. family structures over the last few decades. A New Imputation Methodology (NIM) was used in The objectives of an imputation methodology are the 1996 Canadian Census to carry out Edit and achieved under the NIM by first identifying the passed Imputation (E&I) for these variables. This methodology edit households which are as similar as possible to the allows, for the first time, minimum change imputation of failed edit household. This means that the two households numeric and qualitative variables simultaneously for large should match on as many of the qualitative variables as E&I problems. possible while having small differences between the There exist a variety of imputation methods. Two numeric variables. Households with these characteristics important types are deterministic imputation and hot deck are called nearest neighbours. For each nearest neighbour, imputation. Some imputation methodologies use only the smallest subsets of the non-matching variables which, deterministic imputation or only hot deck imputation, if imputed, allow the household to pass the edits, are while others incorporate the two types of imputation. The identified. One of these imputation actions which passes NIM is a hot deck imputation methodology that uses the edits and resembles both the failed edit household and some deterministic imputation in a prederive module. the passed edit household is then randomly selected. In Section 2, the objectives of an imputation The E&I system, called CANEDIT, used in the 1976 methodology are presented as well as the basic concepts to 1991 Censuses, is based on the imputation of the NIM. In Section 3, some common response errors methodology proposed by Fellegi and Holt (1976). are described and illustrated by examples. Section 4 CANEDIT, unlike the NIM, first determined the presents the major innovation in the editing of couples minimum number of variables to impute and then compared to previous censuses. Also, examples of searched for a nearest neighbour. Reversing the order of imputation actions are provided to illustrate how the NIM the operations allows the NIM to solve larger imputation works. Finally, Section 5 provides some concluding problems. remarks. In 1996, 1% of the private households of the More information on the NIM is available in Atlantic Provinces were households with total non- Bankier, Luc, Nadeau and Newcombe (1996). response while 10% of the households failed because of partial non-response only. Only 2% of the private 2. OBJECTIVES AND OVERVIEW OF THE households of these provinces had one or more variables NIM imputed because of inconsistencies. The objectives of an automated hot deck imputation 3. FREQUENT RESPONSE ERRORS methodology should be as follows: (a) The imputed household should closely resemble In the households that failed because of the failed edit household. inconsistencies, some common response errors are (b) The imputed data for a household should come observed. First, Person l's spouse is sometimes reported from a single donor, if possible, rather than two or more as a son/daughter. In the households with such an error, donors. In addition, the imputed household should closely the difference between the age of Person 1 and the age of 389 the "erroneous" son/daughter, is smaller than the accepted Table 3: NIM Imputation Action for Household of difference between the age of a parent and the age of a Table 1 child. Another frequent situation, which is not an error Relationship Marital Status C-Law Age but which needs to be dealt with carefully, is when Person Status l's spouse is not in position 2 in the household. If it is not Person 1 Married NO 35 possible to identify this person as Person l's spouse and Son Single NO 8 then make sure that the marital status and common-law Daughter Single NO 12 status of this person and of Person 1 are appropriate, there Son Single NO 15 could be a loss of legitimate couples. The household Pl's wife Married NO 36 displayed in Table 1 illustrates the two problems described. In this household, Person l's spouse is reported Another frequent situation are single son/daughters- as a son/daughter and, moreover, this person is in position in-law not living in a common-law relationship. These 5. son/daughters-in-law are also sometimes younger than 15 Table 1: Person l's spouse Reported as years old. Based on the structure of the households, it is Son/dauehter and not in Position 2 suspected that these son/daughters-in-law are in fact step- Relationship Marital C-Law Age son/daughters. The household displayed in Table 4 Status Status illustrates this situation. Person 1 Divorced NO 35 Son Single NO 8 Table 4: Step-Child Possibly Reported as Daughter Single NO 12 So n/Da ugh te r-i n-la w Son Single NO 15 Relationship Sex Marital C-Law Age Daughter Single NO 36 Status Status Person 1 M Married NO 35 For this household, the minimum change imputation Pl's wife F Married NO 47 action is to change one variable: either the age of Person Daughter-in-law F Single NO 24 1, the age of the last daughter or the relationship of this Son M Single NO 19 person. With CANEDIT the age of Person 1 was increased (see Table 2). In this imputed household, there In this household, the daughter-in-law in position 3 is only a difference of 9 years between the imputed age of is single and not living in a common-law relationship. Person 1 and the age of the oldest daughter. This is With CANEDIT, couples were not identified (except because the decade of birth was used in the edit rules with Person l's couples and their parents) and the between CANEDIT since it didn't allow the use of numeric person edit rules for couples could not be applied because variables. In 1996, numeric variables can be used, too many rules would have been required. Only within increasing the precision of the edit rules. For this person edit rules were applied, such as "A person household, the NIM changed the relationship of the last reported as a son or daughter-in-law is single and not person to Person l's husband/wife and also changed the living in a common-law relationship". The minimum marital status of Person 1 and of the last person to change imputation action was then to change either the married (see Table 3). More than the minimum number of marital status, the common-law status or the relationship variables was imputed by the NIM while CANEDIT of this person. In 1991, however, the common-law status imputed only one variable. In this situation, imputing the variable was deterministically imputed in a prederive minimum number of variables is not the right decision. module and could not be changed by imputation. Therefore, in 1991, the only two variables that could be Table 2: C.ANEDIT Imputation Action for imputed for this household to pass this edit rule were the Household of Table 1 marital status and the relationship to Person 1. If there Relationship Marital Status C-Law Age was more than one minimum set of variables to impute, Status CANEDIT selected one of them at random. Therefore, in Person I Divorced NO 45 this situation, each of the two variables had one chance in Son Single NO 8 two of being imputed, independently of the plausibility of Daughter Single NO 12 the resulting responses. For this household, CANEDIT Son Single NO 15 changed the marital status of the daughter-in-law to Daughter Single NO 36 married. This imputation action is illustrated in Table 5. The imputed household had a rare combination of responses and CANEDIT had, in this way, inflated a small group in the population. 390 Table 5: CANEDIT Imputation Action for next section. Household of Table 4 Relationship Sex Marital C-Law Age 4. THE E&I SYSTEM: A 2-STEP PROCESS Status Status Person 1 M Married NO 35 The first step is a prederive module, called Pl's wife F Married NO 47 REORDER7, in which potential couples are identified Daughter-in-law F Married NO 24 prior to imputation. The second step is the hot deck Son M Single NO 19 imputation where couple edit rules are applied to the potential couples to confirm whether these pairs are, in On the other hand, with the NIM, couples are fact, couples.