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…

The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in…

Structural equation models are increasingly used as a modeling tool for multivariate time series data in the social and behavioral sciences. Standard error estimators of SEM models, originally developed for independent data, require modifications to accommodate the fact that time series data are inherently dependent. In this article, we extend a…

In this paper we propose an upward correction to the standard error (SE) estimation of theta[subscript ML], the maximum likelihood (ML) estimate of the latent trait in item response theory (IRT). More specifically, the upward correction is provided for the SE of theta[subscript ML] when item parameter estimates obtained from an independent pretest…

Multidimensional computer adaptive testing (MCAT) can provide higher precision and reliability or reduce test length when compared with unidimensional CAT or with the paper-and-pencil test. This study compared five item selection procedures in the MCAT framework for both domain scores and overall scores through simulation by varying the structure…

Reliability captures the influence of error on a measurement and, in the classical setting, is defined as one minus the ratio of the error variance to the total variance. Laenen, Alonso, and Molenberghs ("Psychometrika" 73:443-448, 2007) proposed an axiomatic definition of reliability and introduced the R[subscript T] coefficient, a measure of…

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized…

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen's (Psychometrika 61:109-121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator…

A person fit test based on the Lagrange multiplier test is presented for three item response theory models for polytomous items: the generalized partial credit model, the sequential model, and the graded response model. The test can also be used in the framework of multidimensional ability parameters. It is shown that the Lagrange multiplier…

Multidimensional unfolding methods suffer from the degeneracy problem in almost all circumstances. Most degeneracies are easily recognized: the solutions are perfect but trivial, characterized by approximately equal distances between points from different sets. A definition of an absolutely degenerate solution is proposed, which makes clear that…

The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood factor analysis. Simulations are performed in which t-statistics based upon these jackknife estimates of the standard errors are computed.…

A nonmetric algorithm, pairwise partitioning, is developed to identify feature-based similarity structures. Presents theorems about the validity of the features identified by the algorithm, and reports results of Monte Carlo simulations that estimate the probabilities of identifying valid features for different feature structures and amounts of…

An asymptotic expression for the reliability of a linearly equated test is developed using normal theory. Reliability is expressed as the product of test reliability before equating and an adjustment term that is a function of the sample sizes used to estimate the linear equating transformation. The approach is illustrated. (SLD)

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. (SLD)