Comparison of different estimation methods used in confirmatory factor analyses in non-normal data: A monte carlo study

In social sciences, education, and psychology, it is difficult to obtain distributional assumption. For these reasons, in situations where normality assumptions are not met, it is important to compare the effects of estimation methods used in CFA. So, in this study, it was aimed to compare CFA results obtained from ML, MLR and WLS estimation methods in data sets with different sample sizes where normality assumption is not met. The study was conducted with data produced after Monte Carlo simulations. In this direction, non-normal data sets were produced 300, 500, 1000, 1500 and 2000 sample sizes including 14 items in total; 7 items in the first factor and including 7 items in the second factor. In the study, fit indices were examined in order to find the efficiency of the same model which was tested with different estimation methods and changing sample sizes. Additionally, as a result of CFA conducted using different estimation methods, the average relative bias related to factor loads were calculated. When analyses conducted with three estimation methods with the sample sizes are compared, it was found that the best fit is obtained with the MLR method in small sample size (N=300 and 500). In the comparison of WLS and MLR prediction methods in big sample sizes (1000, 1500 and 2000) where distribution is not normal, WLS estimations were found to give less biased and truer factor estimations compared to MLR estimations. ML showed high level of bias under all sample size in non-normality