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Type I error rates for multi-group confirmatory maximum likelihood factor analysis with ordinal and mixed item format data : a methodology for construct comparability Koh, Kim Hong

Abstract

Construct comparability studies are of importance in the context of test validation for psychological and educational measures. The most commonly used scale-level methodology for evaluating construct comparability is the Multi-Group Confirmatory Factor Analysis (MGCFA). More specifically, the use of normal-theory Maximum Likelihood (ML) estimation method and Pearson covariance matrix in MGCFA has become increasingly common in day-to-day research given that the estimation methods for ordinal variables require large sample sizes and are limited to 20-25 items. The thesis investigated the statistical properties of the ML estimation method and Pearson covariance matrix in two commonly found contexts, measures with ordinal response formats (binary and Likert-type items) and measures with mixed item formats (wherein some of the items are binary and the remainder are of ordered polytomous items). Two simulation studies were conducted to reflect data typically found in psychological measures and educational achievement tests, respectively. The results of Study 1 show that the number of scale points does not inflate the empirical Type I error rates of the ML chi-square difference test when the ordinal variables approximate a normal distribution. Rather, increasing skewness lead to the inflation of the empirical Type I error rates. In Study 2, the results indicate that mixed item formats and sample size combinations have no effect on the inflation of the empirical Type I error rates when the item response distributions are, again, approximately normal. Implications of the findings and future studies were discussed and recommendations provided for applied researchers.

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