Text is a burgeoning data source for psychological researchers, but little methodological research has focused on adapting popular modeling approaches for text to the context of psychological research. One popular measurement model for text, topic modeling, uses a latent mixture model to represent topics underlying a body of documents. Recently,…

Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related to covariates or outcomes. Such models are subject to interpretational confounding, which occurs when fitting the model with covariates or outcomes alters the results for the measurement model. This has…

Causal analyses typically focus on average treatment effects. Yet for substantive research on topics like inequality, interest extends to treatments' distributional consequences. When individuals differ in their responses to treatment, three types of inequality may result. Treatment may shape inequalities between subgroups defined by pretreatment…

Multilevel factor mixture modeling (FMM) is a hybrid of multilevel confirmatory factor analysis (CFA) and multilevel latent class analysis (LCA). It allows researchers to examine population heterogeneity at the within level, between level, or both levels. This tutorial focuses on explicating the model specification of multilevel FMM that considers…

Recently, deep learning has become a pervasive tool in prediction problems for structured and/or unstructured big data in various areas including science and engineering. In particular, deep neural network models (i.e. a basic core model of deep learning) can be viewed as an extension of statistical models by going through the incorporation of…

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…

Ordinary least squares (OLS) regression and orthogonal regression (OR) address different questions and make different assumptions about errors. The OLS regression of Y on X yields predictions of a dependent variable (Y) contingent on an independent variable (X) and minimizes the sum of squared errors of prediction. It assumes that the independent…

Statistical knowledge is required for students in a range of disciplines. However, there are limited educator resources that exist for applying statistics to solve real-world problems. This investigation provides one approach to teaching statistics using entrepreneurial-minded learning (as a way to connect real-world applications and value…

Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based upon several common approaches for handling dependent effect sizes. In a Monte Carlo simulation, we…

Measurement of latent constructs is one of the most challenging tasks in psychological research. Unlike physical variables, latent constructs are not directly observable but are inferred through individuals' responses to a set of items often referred to as measurement instruments, tests, surveys, or assessments. For decades, exploratory factor…

Nonlinear mixed-effects models are models in which one or more coefficients of the growth model enter in a nonlinear manner, such as appearing in the exponent of the growth function. In their applications, the within-individual residuals are often assumed to be independent with constant variance across time, an assumption that implies that the…

It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure that uses the data to determine how much adjustment to perform. The result is a novel analysis with increased…

Notwithstanding a large body of literature on log-linear models and odds ratios, no general marginal-free index of the association in a contingency table has gained a wide acceptance. Building on a framework developed by L. A. Goodman, we put into light the direct links between odds ratios, the Altham index, the intrinsic association coefficient,…

Psychology research often focuses on interactions, and this has deep implications for inference from non-representative samples. For the goal of estimating average treatment effects, we propose to fit a model allowing treatment to interact with background variables and then average over the distribution of these variables in the population. This…

Piecewise GMM with unknown turning points is a new procedure to investigate heterogeneous subpopulations' growth trajectories consisting of distinct developmental phases. Unlike the conventional PGMM, which relies on theory or experiment design to specify turning points a priori, the new procedure allows for an optimal location of turning points…