In this paper, I will review some aspects of psychometric projects that I have been involved in, emphasizing the nature of the work of the psychometricians involved, especially the balance between the statistical and scientific elements of that work. The intent is to seek to understand where psychometrics, as a discipline, has been and where it…

We propose a functional version of extended redundancy analysis that examines directional relationships among several sets of multivariate variables. As in extended redundancy analysis, the proposed method posits that a weighed composite of each set of exogenous variables influences a set of endogenous variables. It further considers endogenous…

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…

This paper is concerned with supplementing statistical tests for the Rasch model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at a predetermined level by basing the test on the appropriate number of observations.…

"Improper linear models" (see Dawes, Am. Psychol. 34:571-582, "1979"), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of "improper" linear models as "proper" statistical models with a single predictor. We…

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…

This paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory. Paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee. We demonstrate that when three or more ability dimensions are being used, paradoxical results can be induced by…

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

Facial electromyography (EMG) is a useful physiological measure for detecting subtle affective changes in real time. A time series of EMG data contains bursts of electrical activity that increase in magnitude when the pertinent facial muscles are activated. Whereas previous methods for detecting EMG activation are often based on deterministic or…

The generalized logit-linear item response model (GLLIRM) is a linearly constrained nominal categories model (NCM) that computes the scale and intercept parameters for categories as a weighted sum of basic parameters. This paper addresses the problems of the identifiability of the basic parameters and the equivalence between different GLLIRM…

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

Nested logit item response models for multiple-choice data are presented. Relative to previous models, the new models are suggested to provide a better approximation to multiple-choice items where the application of a solution strategy precedes consideration of response options. In practice, the models also accommodate collapsibility across all…

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…