This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

A Monte Carlo simulation was performed to compare methods for handling missing data in growth mixture models. The methods considered in the current study were (a) a fully Bayesian approach using a Gibbs sampler, (b) full information maximum likelihood using the expectation-maximization algorithm, (c) multiple imputation, (d) a two-stage multiple…

Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level…

In order to evaluate the effect of a policy or treatment with pre- and post-treatment outcomes, we propose an approach based on a transition model, which may be applied with multivariate outcomes and accounts for unobserved heterogeneity. This model is based on potential versions of discrete latent variables representing the individual…

The social relations model (SRM) is a mathematical model that can be used to analyze interpersonal judgment and behavior data. Typically, the SRM is applied to one (i.e., univariate SRM) or two variables (i.e., bivariate SRM), and parameter estimates are obtained by employing an analysis of variance method. Here, we present an extension of the SRM…

Nondichotomous response models have been of greater interest in recent years due to the increasing use of different scoring methods and various performance measures. As an important alternative to dichotomous scoring, the use of continuous response formats has been found in the literature. To assess finer-grained skills or attributes and to…

Cognitive diagnosis models (CDMs) are an increasingly popular method to assess mastery or nonmastery of a set of fine-grained abilities in educational or psychological assessments. Several inference techniques are available to quantify the uncertainty of model parameter estimates, to compare different versions of CDMs, or to check model…

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and…

The purpose of this article is to introduce and review the capability and performance of the Stata item response theory (IRT) package that is available from Stata v.14, 2015. Using a simulated data set and a publicly available item response data set extracted from Programme of International Student Assessment, we review the IRT package from…

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…