The problem of inferring the validity of a selection test (x) as a predictor of some criterion (y) when complete xy data are not available is investigated. The basic approach is to construct the predictive probability distribution of the unobserved y scores and then derive interval estimates of the least squares regression weights, the difference in average y scores for selected and unselected cases, and the residual variance in predicting y from x. Further, an approximation to the predictive distribution of the squared correlation between x and y in a future group is derived.

Tests or personal inventories with differential item response weights may be scored by means of punch card equipment. Detailed instructions are given for preparing the cards and scoring the forms. The scoring speed is approximately four to eight times that attained by manual scoring.

In social, behavioral and economic sciences, researchers are interested in modeling a social network among a group of individuals, along with their attributes. The attributes can be responses to survey questionnaires and are often high dimensional. We propose a joint latent space model (JLSM) that summarizes information from the social network and the multivariate attributes in a person-attribute joint latent space. We develop a variational Bayesian expectation–maximization estimation algorithm to estimate the attribute and person locations in the joint latent space. This methodology allows for effective integration, informative visualization and prediction of social networks and attributes. Using JLSM, we explore the French financial elites based on their social networks and their career, political views and social status. We observe a division in the social circles of the French elites in accordance with the differences in their attributes. We analyze user networks and behaviors in multimodal social media systems like YouTube. A R package “jlsm” is developed to fit the models proposed in this paper and is publicly available from the CRAN repository https://cran.r-project.org/web/packages/jlsm/jlsm.pdf.

Although probit analysis has been applied in the field of psychometrics, its use has been restricted by the requirement of linear regression of probits on the independent variate. This paper shows that polynomial probit analysis, a natural extension of the idea of probit analysis, can sometimes overcome the difficulty of a nonlinear plot and does not involve excessive computational labor.

The possibility of obtaining locally optimal solutions with categorical data is pointed out for the original version of OSMOD development by Saito and Otsu. A revision of the initialization strategy in OSMOD is suggested, and its effectiveness in diminishing this possibility is demonstrated.

Constrained fourth-order latent differential equation (FOLDE) models have been proposed (e.g., Boker et al. 2020) as alternative to second-order latent differential equation (SOLDE) models to estimate second-order linear differential equation systems such as the damped linear oscillator model. When, however, only a relatively small number of measurement occasions T are available (i.e., T = 50), the recommendation of which model to use is not clear (Boker et al. 2020). Based on a data set, which consists of T = 56 observations of daily stress for N = 44 individuals, we illustrate that FOLDE can help to choose an embedding dimension, even in the case of a small T. This is of great importance, as parameter estimates depend on the embedding dimension as well as on the latent differential equations model. Consequently, the wavelength as quantity of potential substantive interest may vary considerably. We extend the modeling approaches used in past research by including multiple subjects, by accounting for individual differences in equilibrium, and by including multiple instead of one single observed indicator.

Lyu et al. (Psychometrika, 2023) demonstrated that item-specific factors can cause spurious effects on the structural parameters of IRTree models for multiple nested response processes per item. Here, we discuss some boundary conditions and argue that person selection effects on item parameters are not unique to item-specific factors and that the effects presented by Lyu et al. (Psychometrika, 2023) may not generalize to the family of IRTree models as a whole. We conclude with the recommendation that IRTree model specification should be guided by theoretical considerations, rather than driven by data, in order to avoid misinterpretations of parameter differences.

Given a positive definite covariance matrix $\widehat{\mathrm{\Sigma }}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\widehat{\Sigma }$$\end{document} of dimension n, we approximate it with a covariance of the form $H{H}^{\top }+D$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$HH^\top +D$$\end{document}, where H has a prescribed number $k<n$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k<n$$\end{document} of columns and $D>0$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$D>0$$\end{document} is diagonal. The quality of the approximation is gauged by the I-divergence between the zero mean normal laws with covariances $\widehat{\mathrm{\Sigma }}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\widehat{\Sigma }$$\end{document} and $H{H}^{\top }+D$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$HH^\top +D$$\end{document}, respectively. To determine a pair (H, D) that minimizes the I-divergence we construct, by lifting the minimization into a larger space, an iterative alternating minimization algorithm (AML) à la Csiszár–Tusnády. As it turns out, the proper choice of the enlarged space is crucial for optimization. The convergence of the algorithm is studied, with special attention given to the case where D is singular. The theoretical properties of the AML are compared to those of the popular EM algorithm for exploratory factor analysis. Inspired by the ECME (a Newton–Raphson variation on EM), we develop a similar variant of AML, called ACML, and in a few numerical experiments, we compare the performances of the four algorithms.

Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings.