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...

Normal-distribution-based maximum likelihood (NML) is most widely used for missing data analysis although real data seldom follow a normal distribution. When missing values are missing at random (MAR), recent results indicate that NML estimates (NMLEs) are still consistent for nonnormally...

When missing data are either missing completely at random (MCAR) or missing at random (MAR), the maximum likelihood (ML) estimation procedure preserves many of its properties. However, in any statistical modeling, the distribution specification for the likelihood function is at best only an...

In a variety of statistical problems one needs to solve an equation in order to get an estimator. We consider the large sample properties of such estimators generated from samples that are not necessarily identically distributed. Very general assumptions that lead to the existence, strong...

In a variety of statistical problems one needs to manipulate a sequence of stochastic functions involving some unknown parameters. The asymptotic behavior of the estimated parameters often depends on the asymptotic properties of such functions. Especially, the consistency of the estimated...

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...