THE IMPACT OF WEIGHTING DATA ON SOME FIT INDICES OF STRUCTURAL EQUATION MODELS: A SIMULATION STUDY

The structure equation model (SEM) is a multivariate technique for studying relationships among a set of substantively meaningful variables. The question as to which model best fits the data well, reflects the underlying theory, known as model fit, and is by no means much agreed upon. The present study aims at studying the effects of weights used in transforming the original data to improve model fit indices within the framework of SEM. The weighted values ranged from 0.1 to 0.95; and varying sample sizes (50, 100, 200, 500, and 1000) were used in the present study. Moreover, the study also examines the performance of the weighted values across the symmetric, positive, and negative skewed distributions. To achieve this goal, a Monte Carlo simulation study was carried out using Python, with 500 iterations performed for each weight and sample size. The results show that the p-value gets better in the weighted data in comparison with the values in the case of the original data, with the weights W = [0.2, 0.8] for the left-skewed distributions, W = [0.3, 0.9] for the symmetrical distributions and W = [0.75, 0.85] for the right-skewed distributions. Also, the results show that the larger the sample size, the greater the number of cases that achieve a better p-value with the weighted data. The results also show that the values of goodness of fit index (GFI) and root mean square error of approximation (RMSEA) get better in the weighted data in comparison with the values of the case of the original data, with the weights W = [0.1, 0.2] boolean OR W = [0.8, 0.9] for the left-skewed distributions, W = [0.3, 0.15] boolean OR W = [0.9, 0.95] for the symmetrical distributions and W = [0.7, 0.85] for the right-skewed distributions. Also, the results show that the larger the sample size, the lower the number of cases that achieve better GFI and RMSEA with the weighted data.