Alternative estimation methods in structural equation modeling with LISREL-7: Effects of noncontinuity and nonnormality of variables with varying sample sizes

The accuracy of alternative estimation methods (i.e., ML, GLS, and WLS) in structural equation modeling was investigated under two kinds of sample sizes--150 and 500--with advantage of Monte Carlo study. Four types of variables--continuous-normal, continuous-nonnormal, discrete-normal, and discrete-nonnormal--and their appropriate input matrices were used.Regarding the effects of sample size, in general, the sample size of 500 seemed to alleviate serious distortions in estimation for parameters, standard errors, and $\chi\sp2$ goodness-of-fit measures, whereas a sample size of 150 usually produced untrustworthy results. Regarding the influence of categorization, the categorization of continuous variable caused information loss as the number of categories decreased. The more categories, the less the loss. Regarding the effectiveness of polychoric correlation matrix, the use of polychoric matrix with 7-category variables was effective, but not with 2-category variables. Regarding the influence of nonnormality, the quality of outcomes, as a whole, tended to deteriorate as the degree of nonnormality increased. Regarding model variations, nonnormality with dependent variables was about the same as nonnormality with independent variables. However, nonnormality with dependent and independent variables was the worst. To put it differently, as the number of nonnormal variables increased, outcomes became worse. Regarding the alternative estimation methods, ML and GLS were always better than WLS. WLS exhibited poor performance in dealing with discrete and nonnormal variables.U of I OnlyETDs are only available to UIUC Users without author permissio