Researchers in the field of network psychometrics often focus on the estimation of Gaussian graphical models (GGMs)—an undirected network model of partial correlations—between observed variables of cross-sectional data or single-subject time-series data. This assumes that all variables are measured without measurement error, which may be implausible. In addition, cross-sectional data cannot distinguish between within-subject and between-subject effects. This paper provides a general framework that extends GGM modeling with latent variables, including relationships over time. These relationships can be estimated from time-series data or panel data featuring at least three waves of measurement. The model takes the form of a graphical vector-autoregression model between latent variables and is termed the ts-lvgvar when estimated from time-series data and the panel-lvgvar when estimated from panel data. These methods have been implemented in the software package psychonetrics, which is exemplified in two empirical examples, one using time-series data and one using panel data, and evaluated in two large-scale simulation studies. The paper concludes with a discussion on ergodicity and generalizability. Although within-subject effects may in principle be separated from between-subject effects, the interpretation of these results rests on the intensity and the time interval of measurement and on the plausibility of the assumption of stationarity.

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.

Complex problem solving (CPS) is an up-and-coming twenty-first century skill that requires test-takers to solve dynamically changing problems, often assessed using computer-based tests. The log data that users produce when interacting with a computer-based test provide valuable information about each individual behavioral action they undertake, but such data are rather difficult to handle from a statistical point of view. This paper addresses this issue by building upon recent research focused on decoding log data and aims to identify homogeneous student profiles with regard to their ability to solve CPS tasks. Therefore, we estimated a discrete two-tier item response theory model, which allowed us to profile units (i.e., students) while taking into account the multidimensionality of the data and the explanatory effect of individual characteristics. The results indicate that: (1) CPS can be thought of as a three-dimensional latent variable; (2) there are ten latent classes of students with homogenous profiles regarding the CPS dimensions; (3) students in the higher latent classes generally demonstrate higher cognitive and non-cognitive performances; (4) some of the latent classes seem to profit from learning-by-doing within tasks, whereas others seem to exhibit the reverse behavior; (5) cognitive and non-cognitive skills, as well as gender and to some extent age, contribute to distinguishing among the latent classes.

We generalize the power divergence (PD) family of statistics to the two-parameter logistic IRT model for the purpose of constructing hypothesis tests and confidence intervals of the person parameter. The well-known score test statistic is a special case of the proposed PD family. We also prove the proposed PD statistics are asymptotically equivalent and converge in distribution to ${\chi }_1^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\chi _{1}^2$$\end{document}. In addition, a moment matching method is introduced to compare statistics and choose the optimal one within the PD family. Simulation results suggest that the coverage rate of the associated confidence interval is well controlled even under small sample sizes for some PD statistics. Compared to some other approaches, the associated confidence intervals exhibit smaller lengths while maintaining adequate coverage rates. The utilities of the proposed method are demonstrated by analyzing a real data set.

The tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector. However, when the underlying vector is not normal, the tetrachoric correlation will be different from the underlying correlation. Since assuming underlying normality is often done on pragmatic and not substantial grounds, the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling. This motivates studying the range of latent correlations that are compatible with given binary data, when the distribution of the latent vector is partly or completely unknown. We show that nothing can be said about the latent correlations unless we know more than what can be derived from the data. We identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known. Also, we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations. Implications for tests of underlying normality are briefly discussed.

We propose a dyadic Item Response Theory (dIRT) model for measuring interactions of pairs of individuals when the responses to items represent the actions (or behaviors, perceptions, etc.) of each individual (actor) made within the context of a dyad formed with another individual (partner). Examples of its use include the assessment of collaborative problem solving or the evaluation of intra-team dynamics. The dIRT model generalizes both Item Response Theory models for measurement and the Social Relations Model for dyadic data. The responses of an actor when paired with a partner are modeled as a function of not only the actor’s inclination to act and the partner’s tendency to elicit that action, but also the unique relationship of the pair, represented by two directional, possibly correlated, interaction latent variables. Generalizations are discussed, such as accommodating triads or larger groups. Estimation is performed using Markov-chain Monte Carlo implemented in Stan, making it straightforward to extend the dIRT model in various ways. Specifically, we show how the basic dIRT model can be extended to accommodate latent regressions, multilevel settings with cluster-level random effects, as well as joint modeling of dyadic data and a distal outcome. A simulation study demonstrates that estimation performs well. We apply our proposed approach to speed-dating data and find new evidence of pairwise interactions between participants, describing a mutual attraction that is inadequately characterized by individual properties alone.

Effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size. Existing effect size indices are developed for particular parametric models or population parameters. Here, we propose a robust effect size index based on M-estimators. This approach yields an index that is very generalizable because it is unitless across a wide range of models. We demonstrate that the new index is a function of Cohen’s d, $R^2$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R^2$$\end{document}, and standardized log odds ratio when each of the parametric models is correctly specified. We show that existing effect size estimators are biased when the parametric models are incorrect (e.g., under unknown heteroskedasticity). We provide simple formulas to compute power and sample size and use simulations to assess the bias and standard error of the effect size estimator in finite samples. Because the new index is invariant across models, it has the potential to make communication and comprehension of effect size uniform across the behavioral sciences.

Problem solving has been recognized as a central skill that today’s students need to thrive and shape their world. As a result, the measurement of problem-solving competency has received much attention in education in recent years. A popular tool for the measurement of problem solving is simulated interactive tasks, which require students to uncover some of the information needed to solve the problem through interactions with a computer-simulated environment. A computer log file records a student’s problem-solving process in details, including his/her actions and the time stamps of these actions. It thus provides rich information for the measurement of students’ problem-solving competency. On the other hand, extracting useful information from log files is a challenging task, due to its complex data structure. In this paper, we show how log file process data can be viewed as a marked point process, based on which we propose a continuous-time dynamic choice model. The proposed model can serve as a measurement model for scaling students along the latent traits of problem-solving competency and action speed, based on data from one or multiple tasks. A real data example is given based on data from Program for International Student Assessment 2012.