The Comparison of WLS and Robust WLS Methods in Different Sample Size and Distribution Conditions

Abstract

In structural equation modeling parameter estimation methods vary according to whether data is continuous or ordinal and the normality of distribution. When working with ordinal data, the most commonly used parameter estimation method is WLS (weighted least square), the advantage of which is not requiring any assumption, as the disadvantage of it is requiring large samples. Recently, while Robust estimation methods, WLSM and WLSMV, are commonly used, it is important to see whether they are alternative to WLS in different distribution and sample size conditions. In this study, it is based on the model with five factor model aboüt stüdents’ attitüdes towards mathematics in PISA 2012. The performance of parameter estimation methods including WLS, WLSM, and WLSMV were compared in four different sample sizes (N=200, 500, and 1000) and 3 different distribution types (Sk=0,00; 1,00, and 1,50). As a result, it was seen that WLSMV method has better fit indices than WLSM and WLS methods in different sample size conditions, especially in small sample size condition it is an alternative to WLS method. When it was examined WLS, WLSM, and WLSMV estimation methods according to skewness of distribution, it was seen that the most robust method to skewness of distribution is WLSMV.