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...

We consider maximum likelihood (ML) estimation of mean and covariance structure models when data are missing. Expectation maximization (EM), generalized expectation maximization (GEM), Fletcher-Powell, and Fisher-scoring algorithms are described for parameter estimation. It is shown how the...

Using explicit formulas for the information matrix of ML factor analysis under multivariate normal theory, gross and net information for estimating the parameters in a covariance structure gained by adding the associated mean structure are defined. It is proved that a necessary and sufficient...

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...

Data are called ipsative if they are subject to a constant-sum constraint for each observation. Usually, ipsative data are the consequence of transformation of their corresponding preipsative data. In this article, two kinds of ipsative data are defined. They are the additive ipsative data (AID)...

While latent variable models have been successfully applied in many fields and underpin various modeling techniques, their ability to incorporate categorical responses is hindered due to the lack of accurate and efficient estimation methods. Approximation procedures, such as penalized...

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...

Li's pHd method uses an asymptotic chi-squared test statistic to evaluate a hypothesized dimensionality of a reduced-dimension space in a largely nonparametric setting. This statistic is based on an assumed normal distribution of the predictors. When the distributional assumption is violated, a...