In this paper, we propose a Bayesian causal mediation approach to the analysis of experimental data when both the outcome and the mediator are measured through structured questionnaires based on Likert-scaled inquiries. Our estimation strategy builds upon the error-in-variables literature and, specifically, it leverages Item Response Theory to explicitly model the observed surrogate mediator and outcome measures. We employ their elicited latent counterparts in a simple g-computation algorithm, where we exploit the fundamental identifying assumptions of causal mediation analysis to impute all the relevant counterfactuals and estimate the causal parameters of interest. We finally devise a sensitivity analysis procedure to test the robustness of the proposed methods to the restrictive requirement of mediator's conditional ignorability. We demonstrate the functioning of our proposed methodology through an empirical application using survey data from an online experiment on food purchasing intentions and the effect of different labeling regimes.

Random-intercept cross-lagged panel models (RI-CLPMs) are increasingly used to investigate research questions focusing on how one variable at one time point affects another variable at the subsequent time point. Due to the implied temporal sequence of events in such research designs, interpretations of RI-CLPMs primarily focus on longitudinal cross-lagged paths while disregarding concurrent associations and modeling these only as residual covariances. However, this may cause biased cross-lagged effects. This may be especially so when data collected at the same time point refers to different reference timeframes, creating a temporal sequence of events for constructs measured concurrently. To examine this issue, we conducted a series of empirical analyses in which the impact of modeling or not modeling of directional within-time point associations may impact inferences drawn from RI-CLPMs using data from the longitudinal z-proso study. Results highlight that not considering directional concurrent effects may lead to biased cross-lagged effects. Thus, it is essential to carefully consider potential directional concurrent effects when choosing models to analyze directional associations between variables over time. If temporal sequences of concurrent effects cannot be clearly established, testing multiple models and drawing conclusions based on the robustness of effects across all models is recommended.

Researchers simulating covariance structure models sometimes add model error to their data to produce model misfit. Presently, the most popular methods for generating error-perturbed data are those by Tucker, Koopman, and Linn (TKL), Cudeck and Browne (CB), and Wu and Browne (WB). Although all of these methods include parameters that control the degree of model misfit, none can generate data that reproduce multiple fit indices. To address this issue, we describe a multiple-target TKL method that can generate error-perturbed data that will reproduce target RMSEA and CFI values either individually or together. To evaluate this method, we simulated error-perturbed correlation matrices for an array of factor analysis models using the multiple-target TKL method, the CB method, and the WB method. Our results indicated that the multiple-target TKL method produced solutions with RMSEA and CFI values that were closer to their target values than those of the alternative methods. Thus, the multiple-target TKL method should be a useful tool for researchers who wish to generate error-perturbed correlation matrices with a known degree of model error. All functions that are described in this work are available in the fungible library. Additional materials (e.g., code, supplemental results) are available at https://osf.io/vxr8d/.

Among the most important merits of modern missing data techniques such as multiple imputation (MI) and full-information maximum likelihood estimation is the possibility to include additional information about the missingness process via auxiliary variables. During the past decade, the choice of auxiliary variables has been investigated under a variety of different conditions and more recent research points to the potentially biasing effect of certain auxiliary variables, particularly colliders (Thoemmes & Rose, 2014). In this article, we further extend biasing mechanisms of certain auxiliary variables considered in previous research and thereby focus on their effects on individual diagnosis based on norming, in which the whole distribution of a variable is of interest rather than average coefficients (e.g., means). For this, we first provide the theoretical underpinnings of the mechanisms under study and then provide two focused simulations that (i) directly expand on the collider scenario in Thoemmes and Rose (2014, appendix A) by considering outcomes that are relevant to norming and (ii) extend the scenarios under consideration by instrumental variable mechanisms. We illustrate the bias mechanisms for two different norming approaches and exemplify the procedures by means of an empirical example. We end by discussing limitations and implications of our research.

Despite previous warnings against the use of the difference-in-coefficients method for estimating the indirect effect when the outcome in the mediation model is binary, the difference-in-coefficients method remains readily used in a variety of fields. The continued use of this method is presumably because of the lack of awareness that this method conflates the indirect effect estimate and non-collapsibility. In this paper, we aim to demonstrate the problems associated with the difference-in-coefficients method for estimating indirect effects for mediation models with binary outcomes. We provide a formula that decomposes the difference-in-coefficients estimate into (1) an estimate of non-collapsibility, and (2) an indirect effect estimate. We use a simulation study and an empirical data example to illustrate the impact of non-collapsibility on the difference-in-coefficients estimate of the indirect effect. Further, we demonstrate the application of several alternative methods for estimating the indirect effect, including the product-of-coefficients method and regression-based causal mediation analysis. The results emphasize the importance of choosing a method for estimating the indirect effect that is not affected by non-collapsibility.

The concept of has evolved since it originated in the 1930s as a criterion for the usefulness of the multiple factor model; it has become a form of analysis supporting the validity of inferences about group differences on underlying latent variables. The analysis of (DIF) arose in the literature of item response theory (IRT), where its original purpose was the detection and removal of test items that are differentially difficult for, or biased against, one subpopulation or another. The two traditions merge at the level of the underlying latent variable model, but their separate origins and different purposes have led them to differ in details of terminology and procedure. This review traces some aspects of the histories of the two traditions, ultimately drawing some conclusions about how analysts may draw on elements of both, and how the nature of the research question determines the procedures used. Whether statistical tests are grouped by parameter (as in studies of factorial invariance) or across parameters by variable (as in DIF analysis) depends on the context and is independent of the model, as are subtle aspects of the order of the tests. In any case in which DIF or partial invariance is a possibility, the invariant parameters, or anchor items in DIF analysis, are best selected in an interplay between the statistics and judgment about what is being measured.

To understand psychological data, it is crucial to examine the structure and dimensions of variables. In this study, we examined alternative estimation algorithms to the conventional GLASSO-based exploratory graph analysis (EGA) in network psychometric models to assess the dimensionality structure of the data. The study applied Bayesian conjugate or Jeffreys' priors to estimate the graphical structure and then used the Louvain community detection algorithm to partition and identify groups of nodes, which allowed the detection of the multi- and unidimensional factor structures. Monte Carlo simulations suggested that the two alternative Bayesian estimation algorithms had comparable or better performance when compared with the GLASSO-based EGA and conventional parallel analysis (PA). When estimating the multidimensional factor structure, the analytically based method (i.e., EGA.analytical) showed the best balance between accuracy and mean biased/absolute errors, with the highest accuracy tied with EGA but with the smallest errors. The sampling-based approach (EGA.sampling) yielded higher accuracy and smaller errors than PA; lower accuracy but also lower errors than EGA. Techniques from the two algorithms had more stable performance than EGA and PA across different data conditions. When estimating the unidimensional structure, the PA technique performed the best, followed closely by EGA, and then EGA.analytical and EGA.sampling. Furthermore, the study explored four full Bayesian techniques to assess dimensionality in network psychometrics. The results demonstrated superior performance when using Bayesian hypothesis testing or deriving posterior samples of graph structures under small sample sizes. The study recommends using the EGA.analytical technique as an alternative tool for assessing dimensionality and advocates for the usefulness of the EGA.sampling method as a valuable alternate technique. The findings also indicated encouraging results for extending the regularization-based network modeling EGA method to the Bayesian framework and discussed future directions in this line of work. The study illustrated the practical application of the techniques to two empirical examples in R.

Two research streams on responses to Likert-type items have been developing in parallel: (a) unfolding models and (b) individual response styles (RSs). To accurately understand Likert-type item responding, it is vital to parse unfolding responses from RSs. Therefore, we propose the Unfolding Item Response Tree (UIRTree) model. First, we conducted a Monte Carlo simulation study to examine the performance of the UIRTree model compared to three other models - Samejima's Graded Response Model, Generalized Graded Unfolding Model, and Dominance Item Response Tree model, for Likert-type responses. Results showed that when data followed an unfolding response process and contained RSs, AIC was able to select the UIRTree model, while BIC was biased toward the DIRTree model in many conditions. In addition, model parameters in the UIRTree model could be accurately recovered under realistic conditions, and mis-specifying item response process or wrongly ignoring RSs was detrimental to the estimation of key parameters. Then, we used datasets from empirical studies to show that the UIRTree model could fit personality datasets well and produced more reasonable parameter estimates compared to competing models. A strong presence of RS(s) was also revealed by the UIRTree model. Finally, we provided examples with code for UIRTree model estimation to facilitate the modeling of responses to Likert-type items in future studies.

A popular measure of model fit in structural equation modeling (SEM) is the standardized root mean squared residual (SRMR) fit index. Equivalence testing has been used to evaluate model fit in structural equation modeling (SEM) but has yet to be applied to SRMR. Accordingly, the present study proposed equivalence-testing based fit tests for the SRMR (ESRMR). Several variations of ESRMR were introduced, incorporating different equivalence bounds and methods of computing confidence intervals. A Monte Carlo simulation study compared these novel tests with traditional methods for evaluating model fit. The results demonstrated that certain ESRMR tests based on an analytic computation of the confidence interval correctly reject poor-fitting models and are well-powered for detecting good-fitting models. We also present an illustrative example with real data to demonstrate how ESRMR may be incorporated into model fit evaluation and reporting. Our recommendation is that ESRMR tests be presented in addition to descriptive fit indices for model fit reporting in SEM.

The social relations model (SRM) is the standard approach for analyzing dyadic data stemming from round-robin designs. The model can be used to estimate correlation-coefficients that reflect the overall reciprocity or accuracy of judgements for individual and dyads on the sample- or population level. Within the social relations structural equation modeling framework and on the statistical grounding of stochastic measurement and classical test theory, we show how the multiple indicator SRM can be modified to capture inter-individual and inter-dyadic differences in reciprocal engagement or inter-individual differences in reciprocal accuracy. All models are illustrated on an open-access round-robin data set containing measures of mimicry, liking, and meta-liking (the belief to be liked). Results suggest that people who engage more strongly in reciprocal mimicry are liked more after an interaction with someone and that overestimating one's own popularity is strongly associated with being liked less. Further applications, advantages and limitations of the models are discussed.

Missingness in intensive longitudinal data triggered by latent factors constitute one type of nonignorable missingness that can generate simultaneous missingness across multiple items on each measurement occasion. To address this issue, we propose a multiple imputation (MI) strategy called MI-FS, which incorporates factor scores, lag/lead variables, and missing data indicators into the imputation model. In the context of process factor analysis (PFA), we conducted a Monte Carlo simulation study to compare the performance of MI-FS to listwise deletion (LD), MI with manifest variables (MI-MV, which implements MI on both dependent variables and covariates), and partial MI with MVs (PMI-MV, which implements MI on covariates and handles missing dependent variables full-information maximum likelihood) under different conditions. Across conditions, we found MI-based methods overall outperformed the LD; the MI-FS approach yielded lower root mean square errors (RMSEs) and higher coverage rates for auto-regression (AR) parameters compared to MI-MV; and the PMI-MV and MI-MV approaches yielded higher coverage rates for most parameters except AR parameters compared to MI-FS. These approaches were also compared using an empirical example investigating the relationships between negative affect and perceived stress over time. Recommendations on when and how to incorporate factor scores into MI processes were discussed.

Bias-adjusted three-step latent class (LC) analysis is a popular technique for estimating the relationship between LC membership and distal outcomes. Since it is impossible to randomize LC membership, causal inference techniques are needed to estimate causal effects leveraging observational data. This paper proposes two novel strategies that make use of propensity scores to estimate the causal effect of LC membership on a distal outcome variable. Both strategies modify the bias-adjusted three-step approach by using propensity scores in the last step to control for confounding. The first strategy utilizes inverse propensity weighting (IPW), whereas the second strategy includes the propensity scores as control variables. Classification errors are accounted for using the BCH or ML corrections. We evaluate the performance of these methods in a simulation study by comparing it with three existing approaches that also use propensity scores in a stepwise LC analysis. Both of our newly proposed methods return essentially unbiased parameter estimates outperforming previously proposed methods. However, for smaller sample sizes our IPW based approach shows large variability in the estimates and can be prone to non-convergence. Furthermore, the use of these newly proposed methods is illustrated using data from the LISS panel.

Idiographic measurement models such as p-technique and dynamic factor analysis (DFA) assess latent constructs at the individual level. These person-specific methods may provide more accurate models than models obtained from aggregated data when individuals are heterogeneous in their processes. Developing clustering methods for the grouping of individuals with similar measurement models would enable researchers to identify if measurement model subtypes exist across individuals as well as assess if the different models correspond to the same latent concept or not. In this paper, methods for clustering individuals based on similarity in measurement model loadings obtained from time series data are proposed. We review literature on idiographic factor modeling and measurement invariance, as well as clustering for time series analysis. Through two studies, we explore the utility and effectiveness of these measures. In , a simulation study is conducted, demonstrating the recovery of groups generated to have differing factor loadings using the proposed clustering method. In , an extension of Study 1 to DFA is presented with a simulation study. Overall, we found good recovery of simulated clusters and provide an example demonstrating the method with empirical data.

We implement an analytic approach for ordinal measures and we use it to investigate the structure and the changes over time of self-worth in a sample of adolescents students in high school. We represent the variations in self-worth and its various sub-domains using entropy-based measures that capture the observed uncertainty. We then study the evolution of the entropy across four time points throughout a semester of high school. Our analytic approach yields information about the configuration of the various dimensions of the self together with time-related changes and associations among these dimensions. We represent the results using a network that depicts self-worth changes over time. This approach also identifies groups of adolescent students who show different patterns of associations, thus emphasizing the need to consider heterogeneity in the data.

While Bayesian methodology is increasingly favored in behavioral research for its clear probabilistic inference and model structure, its widespread acceptance as a standard meta-analysis approach remains limited. Although some conventional Bayesian hierarchical models are frequently used for analysis, their performance has not been thoroughly examined. This study evaluates two commonly used Bayesian models for meta-analysis of standardized mean difference and identifies significant issues with these models. In response, we introduce a new Bayesian model equipped with novel features that address existing model concerns and a broader limitation of the current Bayesian meta-analysis. Furthermore, we introduce a simple computational approach to construct simultaneous credible intervals for the summary effect and between-study heterogeneity, based on their joint posterior samples. This fully captures the joint uncertainty in these parameters, a task that is challenging or impractical with frequentist models. Through simulation studies rooted in a joint Bayesian/frequentist paradigm, we compare our model's performance against existing ones under conditions that mirror realistic research scenarios. The results reveal that our new model outperforms others and shows enhanced statistical properties. We also demonstrate the practicality of our models using real-world examples, highlighting how our approach strengthens the robustness of inferences regarding the summary effect.

There has been an increasing call to model multivariate time series data with measurement error. The combination of latent factors with a vector autoregressive (VAR) model leads to the dynamic factor model (DFM), in which dynamic relations are derived within factor series, among factors and observed time series, or both. However, a few limitations exist in the current DFM representatives and estimation: (1) the dynamic component contains either directed or undirected contemporaneous relations, but not both, (2) selecting the optimal model in exploratory DFM is a challenge, (3) the consequences of structural misspecifications from model selection is barely studied. Our paper serves to advance DFM with a hybrid VAR representations and the utilization of LASSO regularization to select dynamic implied instrumental variable, two-stage least squares (MIIV-2SLS) estimation. Our proposed method highlights the flexibility in modeling the directions of dynamic relations with a robust estimation. We aim to offer researchers guidance on model selection and estimation in person-centered dynamic assessments.

When examining whether two continuous variables are associated, tests based on Pearson's, Kendall's, and Spearman's correlation coefficients are typically used. This paper explores modern nonparametric independence tests as an alternative, which, unlike traditional tests, have the ability to potentially detect any type of relationship. In addition to existing modern nonparametric independence tests, we developed and considered two novel variants of existing tests, most notably the Heller-Heller-Gorfine-Pearson (HHG-Pearson) test. We conducted a simulation study to compare traditional independence tests, such as Pearson's correlation, and the modern nonparametric independence tests in situations commonly encountered in psychological research. As expected, no test had the highest power across all relationships. However, the distance correlation and the HHG-Pearson tests were found to have substantially greater power than all traditional tests for many relationships and only slightly less power in the worst case. A similar pattern was found in favor of the HHG-Pearson test compared to the distance correlation test. However, given that distance correlation performed better for linear relationships and is more widely accepted, we suggest considering its use in place or additional to traditional methods when there is no prior knowledge of the relationship type, as is often the case in psychological research.

We present the R package galamm, whose goal is to provide common ground between structural equation modeling and mixed effect models. It supports estimation of models with an arbitrary number of crossed or nested random effects, smoothing splines, mixed response types, factor structures, heteroscedastic residuals, and data missing at random. Implementation using sparse matrix methods and automatic differentiation ensures computational efficiency. We here briefly present the implemented methodology, give an overview of the package and an example demonstrating its use.

How best to model structurally heterogeneous processes is a foundational question in the social, health and behavioral sciences. Recently, Fisher et al. introduced the multi-VAR approach for simultaneously estimating multiple-subject multivariate time series characterized by common and individualizing features using penalized estimation. This approach differs from many popular modeling approaches for multiple-subject time series in that qualitative and quantitative differences in a large number of individual dynamics are well-accommodated. The current work extends the multi-VAR framework to include new adaptive weighting schemes that greatly improve estimation performance. In a small set of simulation studies we compare adaptive multi-VAR with these new penalty weights to common alternative estimators in terms of path recovery and bias. Furthermore, we provide toy examples and code demonstrating the utility of multi-VAR under different heterogeneity regimes using the multivar package for R.

This special issue is a collection of papers inspired by Dr. Molenaar's work and innovations - a tribute to his passion for advancing science and his ability to ignite a spark of creativity and innovation in multiple generations of scientists. Following Dr. Molenaar's creative breadth, the papers address a wide variety of topics - sharing of new methodological developments, ideas, and findings in idiographic science, study of intraindividual variation, behavioral genetics, model inference/identification/selection, and more.