Comparison of Maximum Likelihood, Generalized Least Squares, Ordinary Least Squares, and Asymptotically Distribution Free Parameter Estimates in Drug Abuse Latent Variable Causal Models

Latent variable causal modeling techniques are sometimes criticized when applied to drug abuse data because the commonly-employed maximum likelihood parameter estimation method requires that the data be normally distributed for the statistical tests to be accurate. In this article, four estimators for the parameters in two large latent variable causal models are compared in real drug abuse datasets. One estimator does not require that the data be multivariate normal and does, in fact, correct for data non-normality. Specifically, maximum likelihood and generalized least squares estimators for normally-distributed variables are compared with Browne's asymptotically distribution free techniques for continuous non-normally distributed data. Additionally, ordinary (unweighted) least squares estimates are used. Descriptions of the techniques are given and actual results in two “real” datasets are provided. It is concluded that the distribution free technique provides results which are generally comparable to those obtained with maximum likelihood estimation for datasets which depart in typical ways from the ideal of the multivariate normal distribution.