The normal distribution based likelihood ratio (LR) statistic is widely used in structural equation modeling. Under a sequence of local alternative hypotheses, this statistic has been shown to asymptotically follow a noncentral chi-square distribution. In practice, the population mean vector and...

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures have been developed to analyze such data while taking into account the resulting dependence of observations. Most of these developments require a multivariate normality distribution...

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors...

The maximum likelihood (ML) method, based on the normal distribution assumption, is widely used in mean and covariance structure analysis. With typical nonnormal data, the ML method will lead to biased statistics and inappropriate scientific conclusions. This article develops a simple but...

Normal-distribution-based maximum likelihood (ML) and multiple imputation (MI) are the two major procedures for missing data analysis. This article compares the two procedures with respects to bias and efficiency of parameter estimates. It also compares formula-based standard errors (SEs) for...

Within some classes of nonnormal distributions, we study the asymptotic distribution of the MLE in a covariance structure model based on an incorrect assumption of normality. The asymptotic covariance matrix of the MLE has a similar form as found when the sampling distribution is elliptical,...