What are the advantages and disadvantages of using a maximum likelihood estimation method vs. a least squares estimation method in structural equation modeling?
Monte Carlo simulation studies have shown that under ideal sampling conditions the three most common estimation methods (maximum likelihood, generalized least squares, and ordinary least squares) all yield comparable and very good parameter estimates. However, under less-than-ideal sampling conditions, each method has its own strengths and weaknesses. For example, when the assumption of joint multivariate normality is violated, maximum likelihood estimation tends to yield nonoptimal solutions, especially when the sample size falls below N = 200. In general, for effective structural equation modeling, the total sample size should be at least 200, and at least three manifest variables should be included for each latent variable. Each less-than-ideal sampling situation presents a unique set of difficulties. You may want to contact a consultant by email (click HERE for more info) if you believe that your sample is less than ideal. Also, Latent Variable Models, by J. C. Loehlin, 1987, pp. 5
