The estimation of binary responses in factor analysis models is often complicated, because the marginal likelihood involves an intractable integral. When the number of latent variables is large, the dimensionality of a required integral will be high, and thus numerical integration would not be...

Correlation coefficients have many applications for studying the relationship among multivariate observations. Classical inferences on correlation coefficients are mainly based on the normality assumption. This assumption is hardly realistic in the real world, which implies that the procedures...

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...