Single sample approximations are considered for the cross-validation coefficient in the analysis of covariance structures. Results of a random sampling experiment--using data from ability tests administered to high school students (sample sizes 100, 400, and 800)--illustrate the coefficient and adjustment for predictive validity. (SLD)

An alternative to the Rasch model is introduced. It characterizes strength of response according to the ratio of ability and difficulty parameters rather than their difference. Joint estimation and marginal estimation models are applied to two test data sets. (SLD)

The use of hierarchical models in social science research is discussed, with emphasis on causal inference and consideration of the limitations of hierarchical models. The increased use of Gibbs sampling and other Markov-chain Monte Carlo methods in the application of hierarchical models is recommended. (SLD)

The polytomous unidimensional Rasch model with equidistant scoring (rating scale model) is extended so that two parameters are linearly decomposed into certain basic parameters. A conditional maximum likelihood estimation procedure and a likelihood ratio test are presented in the context of the extended model (linear rating scale model). (SLD)

A correlation matrix of 21 structure-of-intellect (SOI) tests taken by 204 Marine officers at a military base in Southern California, which was intended to reflect aptitudes for military leadership, was reanalyzed through exploratory factor analysis and confirmatory maximum likelihood factor analysis. Higher order factors appeared to have…

A procedure for evaluating a variety of rater reliability models is presented. A multivariate linear model is used to describe and assess a set of ratings. Parameters are represented in terms of a factor analytic model, and maximum likelihood methods test the model parameters. Illustrative examples are presented. (SLD)

The sensitivity of marginal maximum likelihood estimation of item and ability (theta) parameters was examined when prior ability distributions were not matched to underlying ability distributions. Thirty sets of 45-item test data were generated. Conditions affecting the accuracy of estimation are discussed. (SLD)

A Monte Carlo study investigated the use of four cross-validation indices with confirmatory factor analysis models. Influences of sample size, loading size, and degree of model misspecification were studied. Larger sample sizes and better specified models result in better cross-validation results. (SLD)

A crossed random effects model is presented that applies to data with a nested structure to provide maximum likelihood estimates through the EM algorithm. The procedure is illustrated in studies of neighborhood and school effects on educational attainment in Scotland and classroom effects on mathematics learning in the United States. (SLD)

Inference is considered for the marginal distribution of "X" when ("X", "Y") has a truncated bivariate normal distribution. The "Y" variable is truncated, but only the "X" values are observed. A sample of 87 Otis test scores is shown to be well described by this model. (SLD)

This article describes a Monte Carlo study of 2 methods for treating incomplete nonnormal data. Skewed, kurtotic data sets conforming to a single structured model, but varying in sample size, percentage of data missing, and missing-data mechanism, were produced. An asymptotically distribution-free available-case (ADFAC) method and structured-model…

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…

A method for incorporating maximum likelihood (ML) estimation into reliability analyses with item-level missing data is outlined. An ML estimate of the covariance matrix is first obtained using the expectation maximization (EM) algorithm, and coefficient alpha is subsequently computed using standard formulae. A simulation study demonstrated that…

In this paper, the efficiency of conditional maximum likelihood (CML) and marginal maximum likelihood (MML) estimation of the item parameters of the Rasch model in incomplete designs is investigated. The use of the concept of F-information (Eggen, 2000) is generalized to incomplete testing designs. The scaled determinant of the F-information…

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…