First Advisor

Merchant, William

Document Type

Dissertation

Date Created

8-2021

Department

College of Education and Behavioral Sciences, Applied Statistics and Research Methods, ASRM Student Work

Embargo Date

8-2023

Abstract

Recent advancements in Bayesian confirmatory factor analysis (BCFA) explored small sample complete case analysis, yet limited research has investigated BCFA in the presence of missing data. Evidence has been provided in support of the use of Bayesian estimation when strong informative prior information is available in complete case small sample analysis. This study explored how BCFA estimation performed in the presence of missing data with various Bayesian prior information criteria and population models. A simulation study design was utilized with five variables controlled in the study; sample size, percent cell missing, simulated population standardized factor loading, number of items per factor in a two-factor population model, and four different estimation methods. Bayesian estimation utilizing default Mplus non-informative priors, weak informative priors, and strong small variance informative priors for factor loadings were compared to the traditional maximum likelihood estimation. There were 144 different combinations of the five controlled variables, simulated with 1000 replications for each combination. The results of this study expanded the known prior dependence of accurate parameter estimates of BCFA into the presence of missing data and follows previous small sample complete case studies. As missing data increased, accuracy of parameter estimates was tied to specification of prior information. The importance of prior specification for covariance between factors, beyond the non-informative prior, was highlighted. Poor standardized between factor correlation estimates were found with more informative factor loading prior specification. This study provides practitioners some guidance on Bayesian estimation when analyzing data sets with missing data.

Extent

378 pages

Rights Statement

Copyright is held by the author.

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