Alternative Multiple Imputation Inference for Categorical Structural Equation Modeling

Abstract

The use of responses from questionnaires is ubiquitous in social and behavioral science research. One side effect of using such data is that researchers must often account for item level missingness. Multiple imputation is one of the most widely used missing data handling techniques, wherein missing data are replaced by plausible values from the their proper posterior distribution given the observed data. Instead of the standard procedure in structural equation modeling (SEM), which requires researchers to fit their model to imputed data sets as many times as the number of imputations and then combine parameter estimates and standard errors at the end, we propose a new and simpler approach that is computationally more convenient. It has a number of additional benefits such as the availability of fit indices. Motivated by Lee and Cai (2012), who proposed an alternative method for statistical inference under MI in SEM with continuous variables, we extend their approach to the case of categorical variables. Within the context of ordered categorical data, the main idea is summarized as follows. Assume we have thresholds and polychoric correlations computed from M imputed data set. Our goal is to perform estimation and inference with these M different thresholds and polychoric correlations. We can easily average the ii thresholds and polychoric correlations; however, the weight matrix for obtaining the correct statistic in CSEM requires reflecting the between-imputation variance on top of simple averaging of asymptotic covariance matrices of the thresholds and polychoric correlations. Finally, applying Browne (1984)'s Proposition 4 leads us to obtain the correct test statistic,T B. We further considerT YB , a small-sample adjustment ofT B (Yuan & Bentler, 1997). We demonstrate our proposed statistics performance and their power to detect model misspecification via simulation studies. In addition, we illustrate our findings with two empirical data sets. iii The thesis of Seung Won Chung is approved.

Missing data: An update on the state of the art.

“…Multiple imputation was not a viable technique for this application when SG2002 was published, but researchers now have the full complement of tools necessary to fit structural equation models to imputed data sets. Recent developments include new methods for assessing global model fit (Chung & Cai, 2019; T. Lee & Cai, 2012; Y.…”

Pooling methods for likelihood ratio tests in multiply imputed data sets.

“…For this reason, future research should evaluate these methods in other contexts (e.g., longitudinal designs, multilevel data) and for specific applications of popular model types (e.g., SEM, multilevel models). In the context of SEM, other methods could also be used to conduct LRTs in multiply imputed data (Lee & Cai, 2012; Chung & Cai, 2019).…”

Labour market crisis management after crisis of 2008 - Intervention expenditure and "Europe 2020" indicators

“…The multiple imputation (MI) proposed by Rubin (1987) was first, selected as a method to address data gaps. Multiple imputation is one of the most widely used missing data management techniques (Chung & Cai, 2018). The method can be applied to virtually any data structure and model type (Allison, 2003).…”