Alternative Multiple Imputation Inference for Categorical Structural Equation Modeling

Abstract

The use of item responses from questionnaire data is ubiquitous in social 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. The traditional multiple imputation approach in structural equation modeling has a number of limitations. Motivated by Lee and Cai’s approach, we propose an alternative method for conducting statistical inference from multiple imputation in categorical structural equation modeling. We examine the performance of our proposed method via a simulation study and illustrate it with one empirical data set.

Keywords:

• Categorical variables
• multiple imputation
• structural equation modeling
• goodness-of-fit test

Article information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was supported by Grant R305D140046 from the Institute of Education Sciences (IES).

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The authors would like to thank the Associate Editor and reviewers for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors' institution or the funding agency is not intended and should not be inferred.

Notes

1 The multi-stage estimator is often referred to as a limited information method as opposed to full information maximum likelihood (Forero & Maydeu-Olivares, 2009) that relies on raw data.

2 We also calculated rejection rates on all converged replications for N = 250, K=2, having the largest portion of Heywood cases. We note that the results do not make a big difference. The largest differences in means, variances, and p-values are 0.178, 4.661, and 0.012, respectively.

3 Since results from the high missing rate condition show a similar pattern as those of the low missing rate condition, we provide only the results of the low missing rate condition. We will provide the full results upon request.

4 The “BIN2ASC” is an independent exe file from PRELIS/LISREL, written in Fortran, available upon request from Scientific Software International – PRELIS/LISREL’s distributor.