The impact of categorization with confirmatory factor analysis

This study investigated the impact of categorization on confirmatory factor analysis (CFA) parameter estimates, standard errors, and 5 ad hoc fit indexes. Models were generated that represented empirical research situations in terms of model size, sample sizes, and loading values. CFA results obtained from analysis of normally distributed, continuous data were compared to results obtained from 5-category Likert-type data with normal distributions. The ordered categorical data were analyzed using the estimators: Weighted Least Squares (WLS; with polychoric correlation [PC] input) and Maximum Likelihood (ML; with Pearson Product-Moment [PPM] input). ML-PPM-based parameter estimates reported moderate levels of negative bias for all conditions, WLS-PC-based standard errors showed high amounts of bias, especially with a small sample size and moderate loading values. With nonnormally distributed, ordered categorical data, ML-PPM-based parameter estimates, standard errors, and factor intercorrelation showed high levels of bias. Bias levels in standard errors were reduced when the Satorra-Bentler (1988) rescaling correction was applied to nonnormal, ordered categorical data. Five ad hoc model fit indexes appeared robust to the majority of study conditions.