Methods for estimating weighted and unweighted parameters and information criteria used in structural equation modeling of ordinal categorical data and comparison of results with different sample sizes

The question "How can Structural Equation Modeling (SEM) be applied to categorical data?" was sought to be answered in this thesis. Also, the effect of different sample sizes on estimation methods such as Weighted Least Squares (WLS) and Robust Weighted Least Squares (WLSMV) that are used in SEM was studied and compared. In addition, the thesis aims to define how information criteria such as the Akaike Information Criterion (AIC) and the Consistent Akaike Information Criterion (CAIC) are calculated when they are used with categorical data and to show how these criteria vary with different sample sizes. Finally, the theoretical material presented in the study was applied to real data and the results were given in the respective tables. In the simulation studies performed with different sample sizes, the simulations were repeated 1000 times and the average values of criteria were calculated. The organization of the simulation study includes a construct of 4 factors, with 4 questions of each that are measured on a five-point Likert scale. WLS and WLSMV estimation methods were used in the simulation. Different sample sizes, ranging from 300 to 5000 were selected. According to the results of the analyses, it has been concluded that the WLSMV estimation technique provides more effective results at lower sample size compared to the WLS estimation. In addition, it was found that as the sample size increases, the efficiency difference between WLSMV and WLS estimation methods gradually decreases. Moreover, it was detected in the simulation study that there is almost no difference between the two methods for sample sizes over 3000.