Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores,…

Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a "hot hand" and a…

We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also…

Most inter-rater reliability studies using nominal scales suggest the existence of two populations of inference: the population of subjects (collection of objects or persons to be rated) and that of raters. Consequently, the sampling variance of the inter-rater reliability coefficient can be seen as a result of the combined effect of the sampling…

Developed a closed form expression for the asymptotic bias of the explained common variance, or the unexplained common variance under assumptions of multivariate normality in minimum rank factor analysis. Findings from existing data sets show that the presented asymptotic statistical inference is based on a recently developed perturbation theory…

Explores posterior analysis in estimating factor score in a confirmatory factor analysis model with polytomous, censored or truncated data, and studies the accuracy of Bayesian estimates through simulation. Results support these Bayesian estimates for statistical inference. (SLD)

Presents a hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The approach combines the flexibility of semiparametric latent class models that assume common parameters for each subpopulation and the parsimony of random effects models that assume normal distributions for the regression parameters.…

Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate normality distribution assumption, which may not be realistic for practical data. It is…

Three analyses of pretest and posttest data are considered: (1) posttest only designs; (2) two-way repeated measures of analysis of variance (ANOVA); and (3) one-way analysis of covariance (ANCOVA). Conditions that ensure legitimacy of inferences about the equality of treatment effects on the latent variable theta are discussed. (SLD)

A 2-facet measurement model is identified, and its coefficient of generalizability (CG) is examined. Three other multifaceted measurement models and their CGs are identified. An empirical investigation of all four procedures is conducted using data from a study of the psychopathology of 71 prison inmates. (SLD)

Multilevel models are proven tools in social research for modeling complex, hierarchical systems. In multilevel modeling, statistical inference is based largely on quantification of random variables. This paper distinguishes among three types of random variables in multilevel modeling--model disturbances, random coefficients, and future response…

The statistical analysis of processing tree models is advanced by showing how the parameters of estimation and hypothesis testing, based on the likelihood functions, can be accomplished by adapting the expectation-maximization (EM) algorithm. The adaptation makes it easy to program a personal computer to accomplish the stages of statistical…

The quality of approximations to first- and second-order moments based on latent ability estimates is discussed. The ability estimates are based on the Rasch or the two-parameter logistic model, and true score theory is used to account for the fact that the basic quantities are estimates. (SLD)

Four measurement designs are presented for use with correlation coefficients corrected, in one variable, for attenuation due to unreliability (partially disattenuated). Associated asymptotic variance/covariance expressions are presented. Empirical simulation results illustrate the satisfactory Type I error control and statistical power of the…

Two psychometric models are presented for evaluating the difficulty of the distractors in multiple-choice items. They are based on the criterion of rising distractor selection ratios, which facilitates interpretation of the subject and item parameters. Statistical inferential tools are developed in a Bayesian framework: modal a posteriori…