DOCSLIB.ORG

The Design Effect: Do We Know All About It?

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Design Effect: Do We Know All About It? Proceedings of the Annual Meeting of the American Statistical Association, August 5-9, 2001 THE DESIGN EFFECT: DO WE KNOW ALL ABOUT IT? Inho Park and Hyunshik Lee, Westat Inho Park, Westat, 1650 Research Boulevard, Rockville, Maryland 20850 Key Words: Complex sample, Simple random where y is an estimate of the population mean (Y ) sample, pps sampling, Point and variance under a complex design with the sample size of n, f is a estimation, Ratio mean, Total estimator 2 = ()− −1∑N − 2 sampling fraction, and S y N 1 i=1(yi Y ) is 1. Introduction the population element variance of the y-variable. In general, the design effect can be defined for any The design effect is widely used in survey meaningful statistic computed from the sample selected sampling for planning a sample design and to report the from the complex sample design. effect of the sample design in estimation and analysis. It The Deff is a population quantity that depends on is defined as the ratio of the variance of an estimator the sample design and the statistic. The same parameter under a sample design to that of the estimator under can be estimated by different estimators and their simple random sampling. An estimated design effect is Deff’s are different even under the same design. routinely produced by sample survey software such as Therefore, the Deff includes not only the efficiency of WesVar and SUDAAN. the design but also the efficiency of the estimator. This paper examines the relationship between the Särndal et al. (1992, p. 54) made this point clear by design effects of the total estimator and the ratio mean defining it as a function of the design (p) and the estimator, under unequal probability sampling. After a θˆ θ brief review on various definitions and practical usage estimator ( ) for the population parameter .Thus, of the design effect, we consider a decomposition of the we may write it as θˆ = θˆ θˆ′ design effect of the total estimator in term of that of the Deff(p, ) Varp ( ) / Varsrswor ( ) (2.2) ratio mean. In addition, a model-assisted method is used to derive some useful approximate formulae, with where θˆ′ is the usual form of estimator for θ under which we make further comparison of the design effects srswor, which is normally different from θˆ .For of the two estimators. The approximate formulae example, to estimate the population mean, one may use derived here are also compared with the well-known θˆ = Kish’s approximate formula (Kish, 1965, 1995). the ratio mean ∑s wi yi / ∑s wi with sampling Finally, we apply our formulae to an artificial weights w but θˆ′ would be the sample mean ∑ y / n . population created from a complex health survey data i s i for illustration. We will see the effect of a particular statistic θˆ on the design effect in Section 3. In particular, we will show 2. Definition and Use of Design Effect in that the Deff for the Hansen-Hurwitz (or Horvitz- Practice Thompson) estimator for the population total can be very different from the ratio mean for the population The precursor of the design effect that has been mean. popularized by Kish (1965) was used by Cornfield Cochran (1977, p. 85) stated “The design effect (1951). He defined the efficiency of a complex has two primary uses – in sample size determination sampling design as the ratio of the variance of a statistic and in appraising the efficiency of more complex under simple random sampling without replacement plans.” These are still main uses of the design effect. (srswor)withasamplesizeofn to the variance of the However, other important uses have emerged; to statistic under the complex design with the same sample compute the effective sample size and to modify the size. The inverse of the ratio defined by Cornfield was inferential statistic in data analysis as Scott and Rao also used by other sampling statisticians. For example, (1981) used the average design effect to modify the Hansen, Hurwitz, and Madow (1953, pp. 259-270) Pearson type χ 2 -test statistic for complex samples. discussed the increase of the variance due to clustering effect of the cluster sampling over srswor. However, the Kish (1992) later advocated using a slightly name, the design effect, or Deff in short was coined and different Deff, which is called Deft and uses the simple defined formally by Kish (1965, Section 8.2, p. 258) as random sampling with replacement (srswr) variance in “the ratio of the actual variance of a sample to the the denominator. His logic was that without- variance of a simple random sample of the same replacement sampling is a part of design and should be numberofelements.”TheDeffforanestimateofthe captured in the definition. Deft is also easier to use for population mean is given by making inferences. Another reason Kish quoted is that the finite population correction factor (1− f ) may be = 2 Deff Var( y) / {(1- f ) S y / n} (2.1) difficult to compute in some situations. The new correlation between the sampling weights and the definition is given by survey variable (y). However, if the correlation is θˆ = θˆ θˆ′ present, the formula must be modified as studied by Deft(p, ) Varp ( ) / Varsrswr ( ) (2.3) Spencer (2000). We also examine this point further along with Spencer’s approximate formulae in or Deft2 ( p,θˆ) = Var (θˆ) / Var (θˆ) . Survey data p srswr Section 4. software such as WesVar and SUDAAN produce However, when one comes to the Horvitz- Deft2 instead of Deff. Thompson type of total estimator, the situation becomes When the population parameter is the total (Y), very different. Particularly, when the weights are poorly the unbiased estimator is the (weighted) sample total, correlated with the y-variable and the weights vary a lot, the design effect for the total estimator can be much ˆ = ∑ namely, Y s wi yi ,where wi is the properly defined greater than that for the ratio mean. In Section 3, we sampling weight and the summation is over the sample analyze this fact in detail for unequal probability s. When the mean is the parameter of interest, it is sampling. usually estimated by the ratio mean, that is, Yˆ = ∑ w y ∑ w . It is a special case of the ratio 3. DecompositionofDesignEffectofSample s i i s i Total Under Unequal Probability Sampling ≡ ∈ estimator, ∑s wi yi ∑s wi xi ,where xi 1 for all i s . One common misconception about the design Consider a sample design (denoted by p )witha ˆ effects of Yˆ and Y is that they in values are similar. sample size of n drawn by unequal probability However, it has been observed that the design effect of sampling with replacement from a finite population U Yˆ , deft 2 ( p,Yˆ) , is much larger than that of the ratio of size N.Let yk denote the y-value of element k and ˆ let pk denote the associated selection probability, mean, deft 2 ( p,Y ) for human populations. For where ∑ p = 1 . Note that the n draws are example, see Kish (1987) and Hansen, Hurwitz, and U k Madow (1953, p. 608). Some explanation can be found independent since sample selection is with replacement. in Särndal et al. (1992, p. 65 and p. 133) who showed If pk are proportional to a positive size measure xk , 2 ∝ that deft ( p,Yˆ) depends on the relative variation of that is, pk xk , then the sampling scheme is the y-variable under Bernoulli sampling and a special probability proportional to size (pps) sampling. case of one-stage cluster sampling. This dependence Let ki represent the element selected on the i-th contradicts what the design effect is intended to draw. Then the Hansen-Hurwitz’s estimator of the finite measure as Kish (1995) explicitly described: “Deft are population total, Y = ∑ y , is given as used to express the effects of sample design beyond the U k n 2 ˆ = 1 elemental variability ( S y / n ), removing both the units Y ∑ yk pk . (3.1) n = i i of measurement and sample size as nuisance i 1 It is easy to see that E (y / p ) = Y and thus Yˆ is parameters. With the removal of S y , the units, and the p ki ki sample size n,thedesigneffectsonthesamplingerrors the average of n unbiased estimators of Y .For are made generalizable (transferable) to other statistics simplicity, we use i to denote ki unless any confusion and to other variables, within the same survey, and even to other surveys.” His statement is loosely true for the arises. The variance of Yˆ can be written as ˆ 1 ratio mean Y , as the usual approximate design effect Var()Yˆ = ∑ p {}()y / p −Y 2 n U i i i formula is independent of a particular y-variable. A (3.2) 2 = 1 −1 − 2 frequently used approximate formula for the Deft of ∑U pi (yi piY) the ratio mean is given by Kish (1987) n (see Särndal et al., 1992, pp. 51-52). 2 ˆ = + ρ − + 2 Deft ( p,Y ) {1 (b 1)}(1 cv w ) (2.4) Now consider the estimation of the finite where p is an unequal probability sampling of clusters population mean, Y = Y / N .Itcanbeestimatedbythe design, ρ is the intraclass correlation (often called ˆ = ˆ ˆ ˆ = n ratio mean Y Y / N where N ∑ = 1 (npi ) is an within cluster homogeneity measure), b is the average i 1 estimator of the population size N. Using Taylor 2 cluster size, and cvw is the relative variance of the linearization, as shown in Särndal et al.
Load more

Recommended publications
  • A Primer for Using and Understanding Weights with National Datasets
    The Journal of Experimental Education, 2005, 73(3), 221–248 A Primer for Using and Understanding Weights With National Datasets DEBBIE L. HAHS-VAUGHN University of Central Florida ABSTRACT. Using data from the National Study of Postsecondary Faculty and the Early Childhood Longitudinal Study—Kindergarten Class of 1998–99, the author provides guidelines for incorporating weights and design effects in single-level analy- sis using Windows-based SPSS and AM software. Examples of analyses that do and do not employ weights and design effects are also provided to illuminate the differ- ential results of key parameter estimates and standard errors using varying degrees of using or not using the weighting and design effect continuum. The author gives recommendations on the most appropriate weighting options, with specific reference to employing a strategy to accommodate both oversampled groups and cluster sam- pling (i.e., using weights and design effects) that leads to the most accurate parame- ter estimates and the decreased potential of committing a Type I error. However, using a design effect adjusted weight in SPSS may produce underestimated standard errors when compared with accurate estimates produced by specialized software such as AM. Key words: AM, design effects, design effects adjusted weights, normalized weights, raw weights, unadjusted weights, SPSS LARGE COMPLEX DATASETS are available to researchers through federal agencies such as the National Center for Education Statistics (NCES) and the National Science Foundation (NSF), to
    [Show full text]
  • Design Effects in School Surveys
    Joint Statistical Meetings - Section on Survey Research Methods DESIGN EFFECTS IN SCHOOL SURVEYS William H. Robb and Ronaldo Iachan ORC Macro, Burlington, Vermont 05401 KEY WORDS: design effects, generalized variance nutrition, school violence, personal safety and physical functions, school surveys, weighting effects activity. The YRBS is designed to provide estimates for the population of ninth through twelfth graders in public and School surveys typically involve complex private schools, by gender, by age or grade, and by grade and multistage stratified sampling designs. In addition, survey gender for all youths, for African-American youths, and for objectives often require over-sampling of minority groups, Hispanic youths. The YRBS is conducted by ORC Macro and the reporting of hundreds of estimates computed for under contract to CDC-DASH on a two year cycle. many different subgroups of interest. Another feature of For the cycle of the YRBS examined in this paper, 57 these surveys that limits the ability to control the precision primary sampling units (PSUs) were selected from within 16 for the overall population and key subgroups simultaneously strata. Within PSUs, at least three schools per cluster is that intact classes are selected as ultimate clusters; thus, spanning grades 9 through 12 were drawn. Fifteen additional the designer cannot determine the ethnicity of individual schools were selected in a subsample of PSUs to represent students nor the ethnic composition of classes. very small schools. In addition, schools that did not span the ORC Macro statisticians have developed the design entire grade range 9 through 12 were combined prior to and weighting procedures for numerous school surveys at the sampling so that every sampling unit spanned the grade national and state levels.
    [Show full text]
  • Computing Effect Sizes for Clustered Randomized Trials
    Computing Effect Sizes for Clustered Randomized Trials Terri Pigott, C2 Methods Editor & Co-Chair Professor, Loyola University Chicago [email protected] The Campbell Collaboration www.campbellcollaboration.org Computing effect sizes in clustered trials • In an experimental study, we are interested in the difference in performance between the treatment and control group • In this case, we use the standardized mean difference, given by YYTC− d = gg Control group sp mean Treatment group mean Pooled sample standard deviation Campbell Collaboration Colloquium – August 2011 www.campbellcollaboration.org 1 Variance of the standardized mean difference NNTC+ d2 Sd2 ()=+ NNTC2( N T+ N C ) where NT is the sample size for the treatment group, and NC is the sample size for the control group Campbell Collaboration Colloquium – August 2011 www.campbellcollaboration.org TREATMENT GROUP CONTROL GROUP TT T CC C YY,,..., Y YY12,,..., YC 12 NT N Overall Trt Mean Overall Cntl Mean T Y C Yg g S 2 2 Trt SCntl 2 S pooled Campbell Collaboration Colloquium – August 2011 www.campbellcollaboration.org 2 In cluster randomized trials, SMD more complex • In cluster randomized trials, we have clusters such as schools or clinics randomized to treatment and control • We have at least two means: mean performance for each cluster, and the overall group mean • We also have several components of variance – the within- cluster variance, the variance between cluster means, and the total variance • Next slide is an illustration Campbell Collaboration Colloquium – August 2011 www.campbellcollaboration.org TREATMENT GROUP CONTROL GROUP Cntl Cluster mC Trt Cluster 1 Trt Cluster mT Cntl Cluster 1 TT T T CC C C YY,...ggg Y ,..., Y YY11,..
    [Show full text]
  • IBM SPSS Complex Samples Business Analytics
    IBM Software IBM SPSS Complex Samples Business Analytics IBM SPSS Complex Samples Correctly compute complex samples statistics When you conduct sample surveys, use a statistics package dedicated to Highlights producing correct estimates for complex sample data. IBM® SPSS® Complex Samples provides specialized statistics that enable you to • Increase the precision of your sample or correctly and easily compute statistics and their standard errors from ensure a representative sample with stratified sampling. complex sample designs. You can apply it to: • Select groups of sampling units with • Survey research – Obtain descriptive and inferential statistics for clustered sampling. survey data. • Select an initial sample, then create • Market research – Analyze customer satisfaction data. a second-stage sample with multistage • Health research – Analyze large public-use datasets on public health sampling. topics such as health and nutrition or alcohol use and traffic fatalities. • Social science – Conduct secondary research on public survey datasets. • Public opinion research – Characterize attitudes on policy issues. SPSS Complex Samples provides you with everything you need for working with complex samples. It includes: • An intuitive Sampling Wizard that guides you step by step through the process of designing a scheme and drawing a sample. • An easy-to-use Analysis Preparation Wizard to help prepare public-use datasets that have been sampled, such as the National Health Inventory Survey data from the Centers for Disease Control and Prevention
    [Show full text]
  • Design Effect
    2005 YOUTH RISK BEHAVIOR SURVEY Design Effect The results from surveys that use samples such as the Youth Risk Behavior Survey (YRBS) are affected by two types of errors: non-sampling error and sampling error. Nonsampling error usually is caused by procedural mistakes or random or purposeful respondent errors. For example, nonsampling errors would include surveying the wrong school or class, data entry errors, and poor question wording. While numerous measures were taken to minimize nonsampling error for the Youth Risk Behavior Survey (YRBS), nonsampling errors are impossible to avoid entirely and difficult to evaluate or measure statistically. In contrast, sampling error can be described and evaluated. The sample of students selected for your YRBS is only one of many samples of the same size that could have been drawn from the population using the same design. Each sample would have yielded slightly different results had it actually been selected. This variation in results is called sampling error and it can be estimated using data from the sample that was chosen for your YRBS. A measure of sampling error that is often reported is the "standard error" of a particular statistic (mean, percentage, etc.), which is the square root of the variance of the statistic across all possible samples of equal size and design. The standard error is used to calculate confidence intervals within which one can be reasonably sure the true value of the variable for the whole population falls. For example, for any given statistic, the value of that statistic as measured in 95 percent of all independently drawn samples of equal size and design would fall within a range of plus or minus 1.96 times the standard error of that statistic.
    [Show full text]
  • Estimation of Design Effects for ESS Round II
    Estimation of Design Effects for ESS Round II Documentation Matthias Ganninger Tel: +49 (0)621-1246-189 E-Mail: [email protected] November 30, 2006 1 Introduction For the calculation of the effective sample size, neff = nnet/deff, as well as for the determination of the required net sample size in round III, nnet-req(III) = n0 × deff, the design effect is calculated based on ESS round II data. The minimum required effective sample size, n0, is 800 for countries with less than 2 Mio. inhabitants aged 15 and over and 1 500 for all other countries. In the above formulas, nnet denotes the net sample size and deff is a com- bination of two separate design effects: firstly, the design effect due to un- equal selection probabilities, deffp, and, secondly, the design effect due to clustering, deffc. These two quantities, multiplied with each other, then, give the overall design effect according to Gabler et al. (1999): deff = deffp × deffc. This document reports in detail how these quantities are calculated. The remaining part of this section gives an overview of the sampling schemes in the participating countries. In section 2, a description of the preliminary work, foregoing the actual calculation, is given. Then, in section 3, intro- duces the calculation of the design effect due to clustering (deffc) and due to unequal selection probabilities (deffp). The last section closes with some remarks on necessary adjustments of the ESS data to fit the models. The design effects based on ESS round II data are compared to those from round I in section 4.
    [Show full text]
  • Selection Bias in Web Surveys and the Use of Propensity Scores
    WORKING P A P E R Selection Bias in Web Surveys and the Use of Propensity Scores MATTHIAS SCHONLAU ARTHUR VAN SOEST ARIE KAPTEYN MICK P. COUPER WR-279 April 2006 This product is part of the RAND Labor and Population working paper series. RAND working papers are intended to share researchers’ latest findings and to solicit informal peer review. They have been approved for circulation by RAND Labor and Population but have not been formally edited or peer reviewed. Unless otherwise indicated, working papers can be quoted and cited without permission of the author, provided the source is clearly referred to as a working paper. RAND’s publications do not necessarily reflect the opinions of its research clients and sponsors. is a registered trademark. Selection bias in Web surveys and the use of propensity scores Matthias Schonlau1, Arthur van Soest2, Arie Kapteyn1, Mick Couper3 1RAND 2RAND and Tilburg University 3University of Michigan Corresponding author: Matthias Schonlau, RAND, 201 N Craig St, Suite 202, Pittsburgh, PA, 15213 [email protected] Abstract Web surveys have several advantages compared to more traditional surveys with in-person interviews, telephone interviews, or mail surveys. Their most obvious potential drawback is that they may not be representative of the population of interest because the sub-population with access to Internet is quite specific. This paper investigates propensity scores as a method for dealing with selection bias in web surveys. Our main example has an unusually rich sampling design, where the Internet sample is drawn from an existing much larger probability sample that is representative of the US 50+ population and their spouses (the Health and Retirement Study).
    [Show full text]
  • Version 4.1 Effect Size and Standard Error Formulas
    Version 4.1 Effect Size and Standard Error Formulas Ryan Williams, Ph.D. David I. Miller, Ph.D. Natalya Gnedko-Berry, Ph.D. Principal Researcher Researcher Senior Researcher What Works Clearinghouse What Works Clearinghouse What Works Clearinghouse 1 Presenters Ryan Williams, Ph.D. David Miller, Ph.D. What Works Clearinghouse What Works Clearinghouse 2 Learning goals for this webinar • Understand the importance of the new effect size and standard error (SE) formulas for Version 4.1 of the What Works Clearinghouse (WWC) Procedures. • Learn the most frequently used formulas and apply them to examples. • Understand the importance of covariate adjustment in SE calculations. • Understand the Version 4.1 options for clustering adjustments. • Review practical guidance for using the Online Study Review Guide to implement these formulas. 3 Part 1: Importance of effect sizes and standard errors in Version 4.1 1. Introduction of fixed-effects meta-analysis in Version 4.1 2. SEs to weight studies and compute p-values 3. Ongoing work to expand the toolbox of effect size and variance estimators 4 What is a fixed-effects meta-analysis? • Fixed-effects meta-analysis involves computing a weighted average effect size. • Studies are weighted by the inverse of the variance of their effect sizes. • The weights are largely a function of sample size, where larger studies get proportionally more weight in the synthesis. • A key output of this approach is a measure of precision (SE) around the mean effect, which is used, along with the direction of the average effect, to characterize interventions. 5 Effect sizes and standard errors in Version 4.1 • WWC transitioned to a fixed-effects meta-analytic framework in Version 4.1.
    [Show full text]
  • UC Berkeley UC Berkeley Electronic Theses and Dissertations
    UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Methods to Study Intervention Sustainability Using Pre-existing, Community Interventions: Examples from the Water, Sanitation and Hygiene Sector Permalink https://escholarship.org/uc/item/8db349mq Author Arnold, Benjamin Ford Publication Date 2009 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Methods to Study Intervention Sustainability Using Pre-existing, Community Interventions: Examples from the Water, Sanitation and Hygiene Sector by Benjamin Ford Arnold A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Epidemiology in the Graduate Division of the University of California, Berkeley Committee in charge: Professor John M. Colford, Jr., Chair Professor Alan E. Hubbard Professor Kirk R. Smith Fall 2009 Methods to Study Intervention Sustainability Using Pre-existing, Community Interventions: Examples from the Water, Sanitation and Hygiene Sector c 2009 Benjamin Ford Arnold Abstract Methods to Study Intervention Sustainability Using Pre-existing, Community Interventions: Examples from the Water, Sanitation and Hygiene Sector by Benjamin Ford Arnold Doctor of Philosophy in Epidemiology University of California, Berkeley Professor John M. Colford, Jr., Chair This dissertation presents a quasi-experimental study design to evaluate non-randomized, pre-existing community interventions not originally designed to gather rigorous data about sustainability and impact. The core components of the design include selection of a control group using propensity score matching with pre-intervention (baseline) secondary data and post-intervention follow-up in the field. The main advantages of the design include measurement of interventions implemented under actual field conditions (independent of scientific research), as well as the design's ability to gather information about the long term impacts and sustainability of interventions without years of costly prospective follow-up.
    [Show full text]
  • Example of the Impact of Weights and Design Effects on Contingency Tables and Chi-Square Analysis
    Journal of Modern Applied Statistical Methods Copyright © 2003 JMASM, Inc. November, 2003, Vol. 2, No. 2, 425-432 1538 – 9472/03/$30.00 Example Of The Impact Of Weights And Design Effects On Contingency Tables And Chi-Square Analysis David A. Walker Denise Y. Young Educational Research and Assessment Institutional Research Northern Illinois University University of Dallas Many national data sets used in educational research are not based on simple random sampling schemes, but instead are constructed using complex sampling designs characterized by multi-stage cluster sampling and over-sampling of some groups. Incorrect results are obtained from statistical analysis if adjustments are not made for the sampling design. This study demonstrates how the use of weights and design effects impact the results of contingency tables and chi-square analysis of data from complex sampling designs. Key words: Design effect, chi-square, weighting Introduction Methodology Many large-scale data sets used in educational In large-scale data collection, survey research research are constructed using complex designs applies varied sample design techniques. For characterized by multi-stage cluster sampling example, in a single-stage simple random and over-sampling of some groups. Common sample with replacement (SRS), each subject in statistical software packages such as SAS and the study has an equal probability of being SPSS yield incorrect results from such designs selected. Thus, each subject chosen in the unless weights and design effects are used in the sample represents an equivalent total of subjects analysis (Broene & Rust, 2000; Thomas & in the population. More befitting, however, is Heck, 2001). The objective of this study is to that data collection via survey analysis often demonstrate how the use of weights and design involves the implementation of complex survey effects impact the results of contingency tables design (CSD) sampling, such as disproportional and chi-square analysis of data from complex stratified sampling or cluster sampling, where sampling designs.
    [Show full text]
  • Sample Size Calculation and Development of Sampling Plan
    Sample size calculation and development of sampling plan Real population value Overview Bias versus sampling error Level of precision Calculating sampling size • Single survey using random sampling • Single survey using two-stage cluster sampling • Comparing two surveys Drawing the sample • First stage • Second stage Developing a sampling plan Introduction Result from survey is never exactly the same as the actual value in the population WHY? Bias and sampling error Point True estimate population from sample value 45% 50% Total difference = 5 percentage points Sampling Bias error Bias Results from: Enumerator/respondent bias Incorrect measurements (anthropometric surveys) Selection of non-representative sample Likelihood of selection not equal for each sampling unit Sampling error Sampling error Difference between survey result and population value due to random selection of sample Influenced by: • Sample size • Sampling method Unlike bias, it can be predicted, calculated, and accounted for Example 1: Small or large sample? Bias or no bias? Small sample size without bias: Real population value Example 2: Small or large sample? Bias or no bias? Large sample size without bias Real population value Example 3: Small or large sample? Bias or no bias? Large sample size with bias: Real population value Precision versus bias Larger sample size increases precision • It does NOT guarantee absence of bias • Bias may result in very incorrect estimate Quality control is more difficult the larger the sample size Therefore, you may be better off with smaller sample size, less precision, but much less bias. Calculating sample size - Introduction Sample size calculations can tell you how many sampling units you need to include in the survey to get some required level of precision FS & nutrition surveys: sampling considerations If a nutritional survey is conducted as part of CFSVA, additional considerations on sampling are required to reconcile the 2 surveys.
    [Show full text]
  • Conditional Design Effects for SEM Estimates
    Conditional Design Effects for SEM estimates DL Oberski Tilburg University, The Netherlands [email protected] Abstract Discusses “conditional design effects” of different survey error components on structural equation model estimates. Estimates effects of clustering, measurement error, and nonnormality for an application involving reciprocal effects between la- tent variables and correlated error terms. Keywords: latent variable, clustering, stratification, weighting, measurement error, nonnormality. 1 Introduction Structural equation modeling (SEM) is a popular framework for formulating, fitting, and testing an variety of models for continuous data in a wide range of fields. Special cases of SEM include factor analysis, (multivariate) linear regression, path analysis, random growth curve and other longitudinal models, errors-in-variables models, and mediation analysis (Bollen, 1989). This paper discusses a method to evaluate the relative impact of various aspects of the complex sampling design and data on structural equation model parameter estimates. Such “conditional design effects” could serve different purposes: • Given a pilot study, to judge what to improve so as to attain a given standard error for parameters of interest or given power of a hypothesis test; • Given candidate weights, to evaluate their effects conditional on other factors. • To evaluate which “total survey error” components (Groves, 2005) are most rele- vant to particular multivariate models. In particular, we consider the effects of stratification, clustering, unequal probabilities of selection, nonnormality, and measurement error. The remainder of this paper is structured as follows. Section 2 introduces structural equation models (SEM) under complex sampling. It is shown how variance estimators can be defined that omit consideration of each of clustering, stratification, weighting, nonnormality, and measurement error.
    [Show full text]