The robustness of maximum likelihood and distribution-free estimators to non-normality in confirmatory factor analysis

The present Monte Carlo compares the estimates produced by maximum likelihood (ML) and asymptotically distribution-free (ADF) methods. The study extends prior research by investigating the combined effects of sample size, magnitude of correlation among observed indicators, number of indicators, magnitude of skewness and kurtosis, and proportion of indicators with non-normal distributions. Results indicate that both ML and ADF showed little bias in estimates of factor loadings under all conditions studied. As the number of indicators in the model increased, ADF produced greater negative bias in estimates of uniquenesses than ML. In addition, the bias in standard errors for both ML and ADF estimation increased in models with more indicators, and this effect was more pronounced for ADF than ML. Increases in skewness and kurtosis resulted in greater underestimating of standard errors; ML standard errors showed greater bias than ADF under conditions of non-normality, and ML chi-square statistics were also inflated. However, when only half the indicators departed from normality, the inflation in ML chi-square decreased.