Modern regularization and variable selection methods, such as least absolute shrinkage and selection operator (lasso) and Bayesian variable selection, are important tools for psychological researchers to reduce the risk of overfitting, improve prediction in future samples, and increase model interpretability. Although missing data are common in psychological data, it is not straightforward to combine principled methods for addressing missing data with these modern variable selection methods. This challenge is well illustrated in a recent article by Gunn et al. (2023) with a comparison of three approaches for combining lasso with multiple imputation to address missing data. Each of the surveyed approaches results in markedly different results in terms of predictors selected. Their findings underscore limitations of the lasso for the purpose of variable selection. In this article, we show how to implement a Bayesian variable selection method, stochastic search variable selection (SSVS), with multiply imputed data. SSVS is a principled and consistent method for variable selection, and we demonstrate advantages relative to lasso in an example data set and simulation study. It is straightforward to apply an ITS strategy for SSVS using existing software. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Equivalence testing, also called negligible effect significance testing (NEST), is appropriate when a researcher would like to find evidence of a negligible association. However, since equivalence testing/NEST procedures are newer and considerably less popular than traditional difference-based null hypothesis significance testing, it is useful to give a gentle introduction to these methods. Accordingly, this tutorial article aims to provide an overview of NEST/equivalence testing procedures by describing the nature of the procedures, explaining when they should be used, defining what considerations should go into their application (including selecting a minimally meaningful effect size), and outlining how they may be conducted and interpreted. The tutorial article also includes examples and code in open-source software to illustrate how these procedures may be applied to real data. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Psychological theories are often expressed verbally using natural language, which may lead to varying interpretations of the phenomenon under study. This potential confusion can be mitigated by formalizing verbal theories using mathematical language, which can help in defining, analyzing, and interpreting one's hypotheses in quantitative terms. Differential equations (DEs) are a class of models in the dynamical systems framework, particularly suited to many dynamic theories in psychology. However, there is a lack of tools for translating verbal theories into DE systems. To facilitate this translation, we introduce SimDE (https://simde.ucdavis.edu/), an open-access R Shiny application that allows users to specify a DE model and then simulate the trajectories of each variable over time. SimDE provides an interface to simulate a range of DE models, with features such as: (a) first- or second-order DEs (e.g., exponential, oscillatory), (b) models with or without a dynamic error term (ordinary or stochastic DEs), (c) models with coupling dynamics. Users have the flexibility of plotting these systems in order to see the pattern of changes over time and determine the appropriateness of the model for the phenomenon they are trying to study. The goal of our app is to serve as a tool for researchers who want to explore DE models for their psychological theories before they even collect data. It can also help researchers to study the implicit assumptions of their systems defined with such DEs and further refine them as needed. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

A fundamental part of experimental design is to determine the sample size of a study. However, sparse information about population parameters and effect sizes before data collection renders effective sample size planning challenging. Specifically, sparse information may lead research designs to be based on inaccurate a priori assumptions, causing studies to use resources inefficiently or to produce inconclusive results. Despite its deleterious impact on sample size planning, many prominent methods for experimental design fail to adequately address the challenge of sparse a-priori information. Here we propose a Bayesian Monte Carlo methodology for interim design analyses that allows researchers to analyze and adapt their sampling plans throughout the course of a study. At any point in time, the methodology uses the best available knowledge about parameters to make projections about expected evidence trajectories. Two simulated application examples demonstrate how interim design analyses can be integrated into common designs to inform sampling plans on the fly. The proposed methodology addresses the problem of sample size planning with sparse a-priori information and yields research designs that are efficient, informative, and flexible. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Latent moderated structural equation (LMS) is one of the most common techniques for estimating interaction effects involving latent variables (i.e., XWITH command in Mplus). However, empirical applications of LMS often overlook that this estimation technique assumes normally distributed variables and that violations of this assumption may lead to seriously biased parameter estimates. Against this backdrop, we study the robustness of LMS to different shapes and sources of nonnormality and examine whether various statistical tests can help researchers detect such distributional misspecifications. In four simulations, we show that LMS can be severely biased when the latent predictors or the structural disturbances are nonnormal. On the contrary, LMS is unaffected by nonnormality originating from measurement errors. As a result, testing for the multivariate normality of observed indicators of the latent predictors can lead to erroneous conclusions, flagging distributional misspecifications in perfectly unbiased LMS results and failing to reject seriously biased results. To solve this issue, we introduce a novel Hausman-type specification test to assess the distributional assumptions of LMS and demonstrate its performance. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

This article introduces autoregressive (AR) linear models to psychology students and researchers through a step-by-step approach using SPSS and R. Despite their relevance, AR models remain underutilized in behavioral sciences, possibly due to conceptual challenges and difficulties interpreting autocorrelation and seasonality. Our aim is to simplify their implementation by presenting time series models as special cases of linear regression, using accessible language and practical examples. The article illustrates AR estimation using real data, incorporating lagged values as predictors of the dependent variable. Residual diagnostics, a frequently overlooked aspect in applied research, receive special attention, including figures and statistical tests. As Kmenta (1971) demonstrated, serially correlated residuals can lead to artificially low p values for the parameter estimates, potentially resulting in explanatory variables being deemed significant when they truly are not. To promote understanding, we offer intuitive visualizations and clear decision rules for model building, lag selection, and seasonality detection. We compare polynomial and AR models using the confounding test. The data set and annotated R and SPSS scripts are included to support replication and help readers learn basic syntax. We also discuss conceptual and practical limitations of moving average, integration (I), and exponential smoothing models, emphasizing the practical advantages of AR-only models in psychological contexts. Throughout, we stress the importance of aligning statistical models with theoretical assumptions and the temporal structure of data. By combining step-by-step explanations, visual guidance, and real-data applications, this tutorial provides a practical foundation for incorporating AR models into applied psychological research. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Latent growth curve (LGC) models, implemented through structural equation modeling, are widely used to analyze developmental and learning trajectories. Model selection in LGC often relies on goodness-of-fit indices (e.g., χ², Akaike information criterion, and root-mean-square error of approximation), but these metrics fail to assess the temporal constancy, or stability of parameters, an important aspect when forecasting longitudinal data. Addressing this gap, we propose a novel parameter constancy test (PCT) tailored for LGC models. This test evaluates internal constancy, identifies potential breakpoints, helps determine the minimal number of measurement waves needed for reliable modeling, and is also useful for comparing different explanatory models of the analyzed data. To validate this approach, we applied PCT to real-world data, comparing the widely used quadratic function model with the negative exponential model and other nonlinear functions. The results reveal that the negative exponential model, unlike the quadratic function, consistently exhibits parameter constancy even with fewer sampling waves, making it particularly suitable for longitudinal analysis. Additionally, PCT highlights how inappropriate model selection or instability may lead to misinterpretations, particularly in evaluating interventions or extrapolating beyond observed time frames. Our findings emphasize the dual importance of statistical fit and parameter constancy in selecting LGC models. By integrating PCT into standard practice, researchers can better ensure model consistency, optimize resource allocation, and avoid erroneous conclusions in developmental and learning studies. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Several theoretical perspectives suggest that dyadic experiences are distinguished by patterns of behavioral change that emerge during interactions. Methods for examining change in behavior over time are well elaborated for the study of change along continuous dimensions. Extensions for charting increases and decreases in individuals' use of specific, categorically defined behaviors, however, are rarely invoked. Greater accessibility of Bayesian frameworks that facilitate formulation and estimation of the requisite models is opening new possibilities. This article provides a primer on how multinomial logistic growth models can be used to examine between-dyad differences in within-dyad behavioral change over the course of an interaction. We describe and illustrate how these models are implemented in the Bayesian framework using data from support conversations between strangers (N = 118 dyads) to examine (RQ1) how six types of listeners' and disclosers' behaviors change as support conversations unfold and (RQ2) how the disclosers' preconversation distress moderates the change in conversation behaviors. The primer concludes with a series of notes on (a) implications of modeling choices, (b) flexibility in modeling nonlinear change, (c) necessity for theory that specifies how and why change trajectories differ, and (d) how multinomial logistic growth models can help refine current theory about dyadic interaction. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

When comparing relationships between latent variables across groups, measurement invariance (MI) needs to be established to ensure that the test results are valid and meaningful conclusions can be drawn. Common tests of MI are not ideal for investigating many groups and are of limited value during the development of measurement models. In addition, popular network-based alternatives to latent variable modeling lack established methods for MI testing. Therefore, we propose exploratory graph analysis trees (EGA trees) that apply the idea of model-based recursive partitioning to correlation matrices and combine it with EGA-which can be used instead of exploratory factor analysis. In a simulation study, we test the approach regarding its ability to detect configural or metric noninvariance in common factor models given numerous covariates and illustrate its usefulness in conditions with severe violations of configural invaraince based on the diverging number of factors. The results demonstrate that EGA trees can be a valuable tool for the exploration of MI when constructing scales and working on measurement models. We provide R functions within the R package EFAtree to easily implement EGA trees. (PsycInfo Database Record (c) 2025 APA, all rights reserved).