Multivariate Behavioral Research[JOURNAL]
Sun
200 papers
Path and Direction Discovery in Individual Dynamic Factor Models: A Regularized Hybrid Unified Structural Equation Modeling with Latent Variable.
Ye A, Bollen KA
Multivariate Behav Res · 2024 · PMID 39058418 · Publisher ↗
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 whic...
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.
Clustering Individuals Based on Similarity in Idiographic Factor Loading Patterns.
Arizmendi CJ, Gates KM
Multivariate Behav Res · 2025 · PMID 39044482 · Full text
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 f...
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.
An Exact Bayesian Model for Meta-Analysis of the Standardized Mean Difference with Its Simultaneous Credible Intervals.
Lu Y, Zheng Q, Henning K
Multivariate Behav Res · 2024 · PMID 39042102 · Publisher ↗
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. Althoug...
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.
Causal Latent Class Analysis with Distal Outcomes: A Modified Three-Step Method Using Inverse Propensity Weighting.
Lê TT, Clouth FJ, Vermunt JK
Multivariate Behav Res · 2025 · PMID 39034808 · Publisher ↗
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 te...
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.
Multiple Imputation with Factor Scores: A Practical Approach for Handling Simultaneous Missingness Across Items in Longitudinal Designs.
Li Y, Oravecz Z, Ji L … +1 more , Chow SM
Multivariate Behav Res · 2025 · PMID 38997153 · Full text
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 add...
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.
Using Conditional Entropy Networks of Ordinal Measures to Examine Changes in Self-Worth Among Adolescent Students in High School.
Furfaro E, Hsieh F, Weiss MR … +1 more , Ferrer E
Multivariate Behav Res · 2024 · PMID 38997141 · Publisher ↗
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...
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.
Using Monte Carlo Simulation to Forecast the Scientific Utility of Psychological App Studies: A Tutorial.
Kueppers S, Rau R, Scharf F
Multivariate Behav Res · 2024 · PMID 38990138 · Publisher ↗
Mobile applications offer a wide range of opportunities for psychological data collection, such as increased ecological validity and greater acceptance by participants compared to traditional laboratory studies. However,...
Mobile applications offer a wide range of opportunities for psychological data collection, such as increased ecological validity and greater acceptance by participants compared to traditional laboratory studies. However, app-based psychological data also pose data-analytic challenges because of the complexities introduced by missingness and interdependence of observations. Consequently, researchers must weigh the advantages and disadvantages of app-based data collection to decide on the scientific utility of their proposed app study. For instance, some studies might only be worthwhile if they provide adequate statistical power. However, the complexity of app data forestalls the use of simple analytic formulas to estimate properties such as power. In this paper, we demonstrate how Monte Carlo simulations can be used to investigate the impact of app usage behavior on the utility of app-based psychological data. We introduce a set of questions to guide simulation implementation and showcase how we answered them for the simulation in the context of the guessing game app (Rau et al., 2023). Finally, we give a brief overview of the simulation results and the conclusions we have drawn from them for real-world data generation. Our results can serve as an example of how to use a simulation approach for planning real-world app-based data collection.
Integrating Intra- and Interindividual Phenomena in Psychological Theories.
Borsboom D, Haslbeck J
Multivariate Behav Res · 2024 · PMID 38989982 · Publisher ↗
Psychological science is divided into two distinct methodological traditions. One tradition seeks to understand how people function at the individual level, while the other seeks to understand how people differ from each...
Psychological science is divided into two distinct methodological traditions. One tradition seeks to understand how people function at the individual level, while the other seeks to understand how people differ from each other. Methodologies that have grown out of these traditions typically rely on different sources of data. While both use statistical models to understand the structure of the data, and these models are often similar, Molenaar (2004) showed that results from one type of analysis rarely transfer to the other, unless unrealistic assumptions hold. This raises the question how we may integrate these approaches. In this paper, we argue that formalized theories can be used to connect intra- and interindividual levels of analysis. This connection is indirect, in the sense that the relationship between theory and data is best understood through the intermediate level of phenomena: robust statistical patterns in empirical data. To illustrate this, we introduce a distinction between intra- and interindividual phenomena, and argue that many psychological theories will have implications for both types of phenomena. Formalization provides us with a methodological tool for investigating what kinds of intra- and interindividual phenomena we should expect to find if the theory under consideration were true.
Bayesian Analysis of Multi-Factorial Experimental Designs Using SEM.
Langenberg B, Helm JL, Mayer A
Multivariate Behav Res · 2024 · PMID 38984637 · Publisher ↗
Latent repeated measures ANOVA (L-RM-ANOVA) has recently been proposed as an alternative to traditional repeated measures ANOVA. L-RM-ANOVA builds upon structural equation modeling and enables researchers to investigate...
Latent repeated measures ANOVA (L-RM-ANOVA) has recently been proposed as an alternative to traditional repeated measures ANOVA. L-RM-ANOVA builds upon structural equation modeling and enables researchers to investigate interindividual differences in main/interaction effects, examine custom contrasts, incorporate a measurement model, and account for missing data. However, L-RM-ANOVA uses maximum likelihood and thus cannot incorporate prior information and can have poor statistical properties in small samples. We show how L-RM-ANOVA can be used with Bayesian estimation to resolve the aforementioned issues. We demonstrate how to place informative priors on model parameters that constitute main and interaction effects. We further show how to place weakly informative priors on standardized parameters which can be used when no prior information is available. We conclude that Bayesian estimation can lower Type 1 error and bias, and increase power and efficiency when priors are chosen adequately. We demonstrate the approach using a real empirical example and guide the readers through specification of the model. We argue that ANOVA tables and incomplete descriptive statistics are not sufficient information to specify informative priors, and we identify which parameter estimates should be reported in future research; thereby promoting cumulative research.
Parametric g-formula for Testing Time-Varying Causal Effects: What It Is, Why It Matters, and How to Implement It in Lavaan.
Loh WW, Ren D, West SG
Multivariate Behav Res · 2024 · PMID 38963381 · Publisher ↗
Psychologists leverage longitudinal designs to examine the causal effects of a focal predictor (i.e., treatment or exposure) over time. But causal inference of naturally observed time-varying treatments is complicated by...
Psychologists leverage longitudinal designs to examine the causal effects of a focal predictor (i.e., treatment or exposure) over time. But causal inference of naturally observed time-varying treatments is complicated by treatment-dependent confounding in which earlier treatments affect confounders of later treatments. In this tutorial article, we introduce psychologists to an established solution to this problem from the causal inference literature: the parametric g-computation formula. We explain why the g-formula is effective at handling treatment-dependent confounding. We demonstrate that the parametric g-formula is conceptually intuitive, easy to implement, and well-suited for psychological research. We first clarify that the parametric g-formula essentially utilizes a series of statistical models to estimate the joint distribution of all post-treatment variables. These statistical models can be readily specified as standard multiple linear regression functions. We leverage this insight to implement the parametric g-formula using lavaan, a widely adopted R package for structural equation modeling. Moreover, we describe how the parametric g-formula may be used to estimate a marginal structural model whose causal parameters parsimoniously encode time-varying treatment effects. We hope this accessible introduction to the parametric g-formula will equip psychologists with an analytic tool to address their causal inquiries using longitudinal data.
Counterfactual Mediation Analysis with a Latent Class Exposure.
Hammerton G, Heron J, Lewis K … +2 more , Tilling K, Vansteelandt S
Multivariate Behav Res · 2024 · PMID 38821136 · Full text
Latent classes are a useful tool in developmental research, however there are challenges associated with embedding them within a counterfactual mediation model. We develop and test a new method "updated pseudo class draw...
Latent classes are a useful tool in developmental research, however there are challenges associated with embedding them within a counterfactual mediation model. We develop and test a new method "updated pseudo class draws (uPCD)" to examine the association between a latent class exposure and distal outcome that could easily be extended to allow the use of any counterfactual mediation method. UPCD extends an existing group of methods (based on pseudo class draws) that assume that the true values of the latent class variable are missing, and need to be multiply imputed using class membership probabilities. We simulate data based on the Avon Longitudinal Study of Parents and Children, examine performance for existing techniques to relate a latent class exposure to a distal outcome ("one-step," "bias-adjusted three-step," "modal class assignment," "non-inclusive pseudo class draws," and "inclusive pseudo class draws") and compare bias in parameter estimates and their precision to uPCD when estimating counterfactual mediation effects. We found that uPCD shows minimal bias when estimating counterfactual mediation effects across all levels of entropy. UPCD performs similarly to recommended methods (one-step and bias-adjusted three-step), but provides greater flexibility and scope for incorporating the latent grouping within any commonly-used counterfactual mediation approach.
Multilevel Latent Differential Structural Equation Model with Short Time Series and Time-Varying Covariates: A Comparison of Frequentist and Bayesian Estimators.
Cho YW, Chow SM, Marini CM … +1 more , Martire LM
Multivariate Behav Res · 2024 · PMID 38821115 · Full text
Continuous-time modeling using differential equations is a promising technique to model change processes with longitudinal data. Among ways to fit this model, the Latent Differential Structural Equation Modeling (LDSEM)...
Continuous-time modeling using differential equations is a promising technique to model change processes with longitudinal data. Among ways to fit this model, the Latent Differential Structural Equation Modeling (LDSEM) approach defines latent derivative variables within a structural equation modeling (SEM) framework, thereby allowing researchers to leverage advantages of the SEM framework for model building, estimation, inference, and comparison purposes. Still, a few issues remain unresolved, including performance of multilevel variations of the LDSEM under short time lengths (e.g., 14 time points), particularly when coupled multivariate processes and time-varying covariates are involved. Additionally, the possibility of using Bayesian estimation to facilitate the estimation of multilevel LDSEM (M-LDSEM) models with complex and higher-dimensional random effect structures has not been investigated. We present a series of Monte Carlo simulations to evaluate three possible approaches to fitting M-LDSEM, including: frequentist single-level and two-level robust estimators and Bayesian two-level estimator. Our findings suggested that the Bayesian approach outperformed other frequentist approaches. The effects of time-varying covariates are well recovered, and coupling parameters are the least biased especially using higher-order derivative information with the Bayesian estimator. Finally, an empirical example is provided to show the applicability of the approach.
Finite Mixtures of Latent Trait Analyzers With Concomitant Variables for Bipartite Networks: An Analysis of COVID-19 Data.
Failli D, Marino MF, Martella F
Multivariate Behav Res · 2024 · PMID 38784986 · Publisher ↗
Networks consist of interconnected units, known as nodes, and allow to formally describe interactions within a system. Specifically, bipartite networks depict relationships between two distinct sets of nodes, designated...
Networks consist of interconnected units, known as nodes, and allow to formally describe interactions within a system. Specifically, bipartite networks depict relationships between two distinct sets of nodes, designated as sending and receiving nodes. An integral aspect of bipartite network analysis often involves identifying clusters of nodes with similar behaviors. The computational complexity of models for large bipartite networks poses a challenge. To mitigate this challenge, we employ a Mixture of Latent Trait Analyzers (MLTA) for node clustering. Our approach extends the MLTA to include covariates and introduces a double EM algorithm for estimation. Applying our method to COVID-19 data, with sending nodes representing patients and receiving nodes representing preventive measures, enables dimensionality reduction and the identification of meaningful groups. We present simulation results demonstrating the accuracy of the proposed method.
The Effects of Questionnaire Length on the Relative Impact of Response Styles in Ambulatory Assessment.
Hasselhorn K, Ottenstein C, Meiser T … +1 more , Lischetzke T
Multivariate Behav Res · 2024 · PMID 38779850 · Publisher ↗
Ambulatory assessment (AA) is becoming an increasingly popular research method in the fields of psychology and life science. Nevertheless, knowledge about the effects that design choices, such as questionnaire length (i....
Ambulatory assessment (AA) is becoming an increasingly popular research method in the fields of psychology and life science. Nevertheless, knowledge about the effects that design choices, such as questionnaire length (i.e., number of items per questionnaire), have on AA data quality is still surprisingly restricted. Additionally, response styles (RS), which threaten data quality, have hardly been analyzed in the context of AA. The aim of the current research was to experimentally manipulate questionnaire length and investigate the association between questionnaire length and RS in an AA study. We expected that the group with the longer (82-item) questionnaire would show greater reliance on RS relative to the substantive traits than the group with the shorter (33-item) questionnaire. Students ( = 284) received questionnaires three times a day for 14 days. We used a multigroup two-dimensional item response tree model in a multilevel structural equation modeling framework to estimate midpoint and extreme RS in our AA study. We found that the long questionnaire group showed a greater reliance on RS relative to trait-based processes than the short questionnaire group. Although further validation of our findings is necessary, we hope that researchers consider our findings when planning an AA study in the future.
Linear Mixed-Effects Models for Dependent Data: Power and Accuracy in Parameter Estimation.
Liu Y, Hau KT, Liu H
Multivariate Behav Res · 2024 · PMID 38779786 · Publisher ↗
Linear mixed-effects models have been increasingly used to analyze dependent data in psychological research. Despite their many advantages over ANOVA, critical issues in their analyses remain. Due to increasing random ef...
Linear mixed-effects models have been increasingly used to analyze dependent data in psychological research. Despite their many advantages over ANOVA, critical issues in their analyses remain. Due to increasing random effects and model complexity, estimation computation is demanding, and convergence becomes challenging. Applied users need help choosing appropriate methods to estimate random effects. The present Monte Carlo simulation study investigated the impacts when the restricted maximum likelihood (REML) and Bayesian estimation models were misspecified in the estimation. We also compared the performance of Akaike information criterion (AIC) and deviance information criterion (DIC) in model selection. Results showed that models neglecting the existing random effects had inflated Type I errors, unacceptable coverage, and inaccurate -squared measures of fixed and random effects variation. Furthermore, models with redundant random effects had convergence problems, lower statistical power, and inaccurate -squared measures for Bayesian estimation. The convergence problem is more severe for REML, while reduced power and inaccurate -squared measures were more severe for Bayesian estimation. Notably, DIC was better than AIC in identifying the true models (especially for models including person random intercept only), improving convergence rates, and providing more accurate effect size estimates, despite AIC having higher power than DIC with 10 items and the most complicated true model.
Testing Conditional Independence in Psychometric Networks: An Analysis of Three Bayesian Methods.
Sekulovski N, Keetelaar S, Huth K … +4 more , Wagenmakers EJ, van Bork R, van den Bergh D, Marsman M
Multivariate Behav Res · 2024 · PMID 38733319 · Publisher ↗
Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independe...
Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independent given the rest of the network variables. This conditional independence structure is a gateway to understanding the causal structure underlying psychological processes. Thus, it is crucial to have an appropriate method for evaluating conditional independence and dependence hypotheses. Bayesian approaches to testing such hypotheses allow researchers to differentiate between absence of evidence and evidence of absence of connections (edges) between pairs of variables in a network. Three Bayesian approaches to assessing conditional independence have been proposed in the network psychometrics literature. We believe that their theoretical foundations are not widely known, and therefore we provide a conceptual review of the proposed methods and highlight their strengths and limitations through a simulation study. We also illustrate the methods using an empirical example with data on Dark Triad Personality. Finally, we provide recommendations on how to choose the optimal method and discuss the current gaps in the literature on this important topic.
Bayesian Multivariate Logistic Regression for Superiority and Inferiority Decision-Making under Observable Treatment Heterogeneity.
Kavelaars X, Mulder J, Kaptein M
Multivariate Behav Res · 2024 · PMID 38733304 · Full text
The effects of treatments may differ between persons with different characteristics. Addressing such treatment heterogeneity is crucial to investigate whether patients with specific characteristics are likely to benefit...
The effects of treatments may differ between persons with different characteristics. Addressing such treatment heterogeneity is crucial to investigate whether patients with specific characteristics are likely to benefit from a new treatment. The current paper presents a novel Bayesian method for superiority decision-making in the context of randomized controlled trials with multivariate binary responses and heterogeneous treatment effects. The framework is based on three elements: a) Bayesian multivariate logistic regression analysis with a Pólya-Gamma expansion; b) a transformation procedure to transfer obtained regression coefficients to a more intuitive multivariate probability scale (i.e., success probabilities and the differences between them); and c) a compatible decision procedure for treatment comparison with prespecified decision error rates. Procedures for a priori sample size estimation under a non-informative prior distribution are included. A numerical evaluation demonstrated that decisions based on a priori sample size estimation resulted in anticipated error rates among the trial population as well as subpopulations. Further, average and conditional treatment effect parameters could be estimated unbiasedly when the sample was large enough. Illustration with the International Stroke Trial dataset revealed a trend toward heterogeneous effects among stroke patients: Something that would have remained undetected when analyses were limited to average treatment effects.
Methodological and Statistical Practices of Using Symptom Networks to Evaluate Mental Health Interventions: A Review and Reflections.
Schumacher L, Burger J, Echterhoff J … +1 more , Kriston L
Multivariate Behav Res · 2024 · PMID 38733300 · Publisher ↗
The network approach to psychopathology, which assesses associations between individual symptoms, has recently been applied to evaluate treatments for mental disorders. While various options for conducting network analys...
The network approach to psychopathology, which assesses associations between individual symptoms, has recently been applied to evaluate treatments for mental disorders. While various options for conducting network analyses in intervention research exist, an overview and an evaluation of the various approaches are currently missing. Therefore, we conducted a review on network analyses in intervention research. Studies were included if they constructed a symptom network, analyzed data that were collected before, during or after treatment of a mental disorder, and yielded information about the treatment effect. The 56 included studies were reviewed regarding their methodological and analytic strategies. About half of the studies based on data from randomized trials conducted a network intervention analysis, while the other half compared networks between treatment groups. The majority of studies estimated cross-sectional networks, even when repeated measures were available. All but five studies investigated networks on the group level. This review highlights that current methodological practices limit the information that can be gained through network analyses in intervention research. We discuss the strength and limitations of certain methodological and analytic strategies and propose that further work is needed to use the full potential of the network approach in intervention research.
Understanding the Consequences of Collinearity for Multilevel Models: The Importance of Disaggregation Across Levels.
Yaremych HE, Preacher KJ
Multivariate Behav Res · 2024 · PMID 38721945 · Publisher ↗
In multilevel models, disaggregating predictors into level-specific parts (typically accomplished via centering) benefits parameter estimates and their interpretations. However, the importance of level-specificity has be...
In multilevel models, disaggregating predictors into level-specific parts (typically accomplished via centering) benefits parameter estimates and their interpretations. However, the importance of level-specificity has been sparsely addressed in multilevel literature concerning collinearity. In this study, we develop novel insights into the interactivity of centering and collinearity in multilevel models. After integrating the broad literatures on centering and collinearity, we review level-specific and conflated correlations in multilevel data. Next, by deriving formal relationships between predictor collinearity and multilevel model estimates, we demonstrate how the consequences of collinearity change across different centering specifications and identify data characteristics that may exacerbate or mitigate those consequences. We show that when all or some level-1 predictors are uncentered, slope estimates can be greatly biased by collinearity. Disaggregation of all predictors eliminates the possibility that fixed effect estimates will be biased due to collinearity alone; however, under some data conditions, collinearity is associated with biased standard errors and random effect (co)variance estimates. Finally, we illustrate the importance of disaggregation for diagnosing collinearity in multilevel data and provide recommendations for the use of level-specific collinearity diagnostics. Overall, the necessity of disaggregation for identifying and managing collinearity's consequences in multilevel models is clarified in novel ways.
Determining Sample Size Requirements in EFA Solutions: A Simple Empirical Proposal.
Lorenzo-Seva U, Ferrando PJ
Multivariate Behav Res · 2024 · PMID 38717588 · Publisher ↗
In unrestricted or exploratory factor analysis (EFA), there is a wide range of recommendations about the size samples should be to attain correct and stable solutions. In general, however, these recommendations are eithe...
In unrestricted or exploratory factor analysis (EFA), there is a wide range of recommendations about the size samples should be to attain correct and stable solutions. In general, however, these recommendations are either rules of thumb or based on simulation results. As it is hard to establish the extent to which a particular data set suits the conditions used in a simulation study, the advice produced by simulation studies is not direct enough to be of practical use. Instead of trying to provide general and complex recommendations, in this article, we propose to estimate the sample size that is needed to analyze a data set at hand. The estimation takes into account the specified EFA model. The proposal is based on an intensive simulation process in which the sample correlation matrix is used as a basis for generating data sets from a pseudo-population in which the parent correlation holds exactly, and the criterion for determining the size required is a threshold that quantifies the closeness between the pseudo-population and the sample reproduced correlation matrices. The simulation results suggest that the proposal works well and that the determinants identified agree with those in the literature.
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