Maximum Likelihood (ML) and Diagonally Weighted Least Squares (DWLS) Estimation Procedures: A Comparison of Estimation Bias with Ordinal and Multivariate Non-Normal Data

This paper aims to identify the effect of using the maximum likelihood (ML) parameter estimation method when data do not meet the assumption of multivariate normality and are not continuous. Both ML and the diagonally weighted least squares (DWLS) procedure were applied to simulated sets of data, which have different distributions and include variables that can take different numbers of possible values. Results were also compared to the ideal situation of a data set consisting of continuous, normally distributed variables. Outcomes indicate that ML provides accurate results when data are continuous and uniformly distributed, but is not as precise with ordinal data that is not treated as continuous, especially when variables have a small number of categories and data do not meet the assumption of multivariate normality. In contrast, DWLS provides more accurate parameter estimates, and a model fit that is more robust to variable type and non-normality.