Confirmatory factor analysis of ordered categorical variables with large models

This simulation study examined the utility of a categorical variable methodology developed by Muthén (1984) for confirmatory factor analysis of ordinal variables. Multivariate normal data were generated according to four different factor models (4, 9, 15 and 22 parameters) for samples of 500 and 1000. Indicators were classified into Five categories so that manifest variables displayed negative, zero, positive or highly positive kurtosis. Each of the 32 design cells was replicated 100 times. Parameter estimates exhibited little or no bias under any condition. Standard errors were underestimated with respect to the standard deviation of the parameter estimates. This negative bias worsened as model size grew or as positive kurtosis increased; it was more severe for factor correlations than indicator loadings. Chi‐square fit statistics rejected the true model more often than expected for nine‐parameter and larger models. Although variables with high positive kurtosis led to the greatest misfit in large models, fit was poor even with variables of zero kurtosis. As expected, larger samples always yielded more accurate results.