Multivariate Behavioral Research[JOURNAL]
Sun
200 papers
Multi-Group Multidimensional Classification Accuracy Analysis (MMCAA): A General Framework for Evaluating the Practical Impact of Partial Invariance.
Ozcan M, Lai MHC
Multivariate Behav Res · 2026 Mar · PMID 41891771 · Publisher ↗
Measurement invariance (MI) is a prerequisite for the meaningful and valid comparison of test scores across individuals with different group membership. Given that tests are often used in high-stakes contexts (e.g., diag...
Measurement invariance (MI) is a prerequisite for the meaningful and valid comparison of test scores across individuals with different group membership. Given that tests are often used in high-stakes contexts (e.g., diagnosis), the practical impact of violations of MI is of great interest to researchers and practitioners alike. Existing approaches to evaluating the practical impact of noninvariance on selection or classification accuracy have mostly considered MI across two groups. When a population is made up of multiple subpopulations (e.g., ethnic groups), groups are often dichotomized for ease of analysis, which may lead to misleading inferences due to the loss of information and precision. The current paper introduces a general framework for investigating the practical impact of measurement noninvariance on the accuracy and fairness of decisions made using a test administered to individuals from any number of subpopulations. We demonstrate the application and the advantages of the multi-group multidimensional classification accuracy analysis (MMCAA) framework through an illustrative example on the MI of a depression scale across four ethnic groups using a national dataset, showing that valuable information is lost if the grouping variable is collapsed. We offer guidelines for interpretation. The MMCAA framework is fully automated in the R package .
Multivariate Location-Scale Models for Meta-Analysis.
Jansen K, Nestler S
Multivariate Behav Res · 2026 Mar · PMID 41885502 · Publisher ↗
Often, primary studies that are pooled in a meta-analysis provide information on several outcomes of interest. Multivariate meta-analysis allows to analyze these outcomes simultaneously and model their relationship, and...
Often, primary studies that are pooled in a meta-analysis provide information on several outcomes of interest. Multivariate meta-analysis allows to analyze these outcomes simultaneously and model their relationship, and in addition can be more efficient than separate, univariate meta-analyses. However, standard multivariate meta-analysis models typically assume that the between-study variances and correlations are constant across studies. While it is possible to relax this assumption of constant heterogeneity by using location-scale models in univariate meta-analysis, extensions to the multivariate case have not yet been proposed. Here, we fill this gap by describing a location-scale model for the multivariate setting where both the between-study variances of the different outcomes and the correlations between them can depend on covariates. We examine its performance in a simulation study, where we compare univariate and bivariate location-scale models and different estimation methods. In addition, we show how to apply this model to data from a meta-analysis on the effects of motivational reading instruction on reading achievement and motivation. We discuss the implications of our findings for further research on meta-analysis of multiple outcomes and provide recommendations for the use of multivariate location-scale meta-analysis in applications.
Evaluating the Performance of R-Squared Measures in Multilevel Models.
Iglesias D, Sorrel MA, Olmos R
Multivariate Behav Res · 2026 Mar · PMID 41848595 · Publisher ↗
Multilevel Models (MLMs) have become a valuable tool in the behavioral and social sciences, providing a framework for analyzing clustered data structures commonly encountered in these fields. Unlike single-level regressi...
Multilevel Models (MLMs) have become a valuable tool in the behavioral and social sciences, providing a framework for analyzing clustered data structures commonly encountered in these fields. Unlike single-level regression, measures in MLMs become more intricate due to the need to account for sources of variance at different levels. Recently, Rights and Sterba (2019) introduced an integrative framework of MLM measures, providing a unifying approach to interpreting MLM measures in relation to specific substantive questions. While this framework represents a valuable resource for applied research, the measures have been defined in the population, and their performance across various conditions reflecting applied MLM practices remains unexplored. The present study evaluates the performance of the different MLM measures as estimators of their population values through Monte Carlo simulations. Among other factors, we examined how the number of level-1 and level-2 predictors, cross-level interactions, and random slopes affect the accuracy of the corresponding MLM measures. Results indicate that as the number of level-2 predictors increases, a greater number of clusters is required to ensure accurate estimates. The greater the number of level-1 predictors, cross-level interactions, and random slopes, increasing either the number of clusters or the number of observations per cluster leads to more accurate estimates.
A Hierarchical Ordinal Regression Model for Treatment-Reversal Designs with Application to Non-Overlap Effect Sizes.
Uanhoro JO, Rojo M
Multivariate Behav Res · 2026 Mar · PMID 41840958 · Publisher ↗
We present a hierarchical ordinal model for analyzing single-case designs (SCDs), with a focus on treatment-reversal designs. SCDs involve systematic measurement of outcomes for individual cases across different conditio...
We present a hierarchical ordinal model for analyzing single-case designs (SCDs), with a focus on treatment-reversal designs. SCDs involve systematic measurement of outcomes for individual cases across different conditions or phases, aiming to establish causal relations between interventions and behavioral changes. While visual analysis is a common approach in SCDs, the field is increasingly adopting quantitative effect size metrics, such as non-overlap indices, to supplement visual examination. However, statistical theory supporting the use of these indices remains underdeveloped. To address this gap, we developed a Bayesian hierarchical ordinal model that enables the estimation of case-specific non-overlap indices. Through simulation studies, we demonstrate that these indices are more accurate than those obtained standard approaches. Moreover, the model can generate parametric indices with greater accuracy than standard methods. To facilitate the adoption of this model, we provide an R package () for model estimation. This contribution aims to enhance the analysis and interpretation of SCDs, ultimately advancing our understanding of the efficacy of interventions and promoting evidence-based decision-making.
To Disaggregate or Not to Disaggregate: A Focus on Covariates in Multilevel Models.
Mitchell R, Enders CK, Feng Y
Multivariate Behav Res · 2026 Mar · PMID 41800987 · Publisher ↗
It is routinely recommended that level-1 variables in multilevel models be disaggregated when they are of substantive importance. Yet, the consensus on the disaggregation of level-1 covariates is more mixed. Disaggregati...
It is routinely recommended that level-1 variables in multilevel models be disaggregated when they are of substantive importance. Yet, the consensus on the disaggregation of level-1 covariates is more mixed. Disaggregation clarifies interpretation and reduces bias in the covariate, though some methodologists argue that it is unnecessary when the covariate itself is not of substantive interest. Our study builds off recent work to explore the tradeoffs between bias and precision when choosing to disaggregate level-1 covariates when the primary interest lies in a level-2 predictor. Using a Monte Carlo simulation, we examine how factors such as the intraclass correlation, the magnitude of the contextual effect, the within- and between-level effect sizes, the correlation among level-2 effects, sample size at both levels, and the method of disaggregation (manifest versus latent) influence bias, precision, and power of a level-2 focal estimate. Our findings suggest that although disaggregation generally improves interpretability and reduces bias, there are conditions where a non-disaggregated approach may yield greater precision. These insights inform best practices for handling lower-level covariates in multilevel models.It is routinely recommended that level-1 variables in multilevel models be disaggregated when they are of substantive importance. Yet, the consensus on the disaggregation of level-1 covariates is more mixed. Disaggregation clarifies interpretation and reduces bias in the covariate, though some methodologists argue that it is unnecessary when the covariate itself is not of substantive interest. Our study builds off the work of Rights et al. to explore the tradeoffs between bias and precision when choosing to disaggregate level-1 covariates when the primary interest lies in a level-2 predictor. Using a Monte Carlo simulation, we examine how factors such as the intraclass correlation, the magnitude of the contextual effect, the within- and between-level effect sizes, the correlation among level-2 effects, sample size at both levels, and the method of disaggregation (manifest versus latent) influence bias, precision, and power of a level-2 focal estimate. Our findings suggest that although disaggregation generally improves interpretability and reduces bias, there are conditions where a non-disaggregated approach may yield greater precision. These insights inform best practices for handling lower-level covariates in multilevel models.
semfindr: An R Package for Identifying Influential Cases in Structural Equation Modeling.
Cheung SF, Lai MHC
Multivariate Behav Res · 2026 Mar · PMID 41770577 · Publisher ↗
Measuring case influence on parameter estimates and model fit measures, which is one type of sensitivity analysis, is important for assessing the robustness of findings in structural equation modeling (SEM). However, it...
Measuring case influence on parameter estimates and model fit measures, which is one type of sensitivity analysis, is important for assessing the robustness of findings in structural equation modeling (SEM). However, it was rarely reported clearly or was conducted inappropriately, mistaking outlier detection for influential cases assessment. Some existing tools have limitations in the models or estimation methods they support, or in the types of influence measures that can be computed. We developed an easy-to-use R package, semfindr, for identifying influential cases in SEM using the leave-one-out (LOO) method. It reduces the computational cost by separating the refitting step from the case influence computation step. It also has various plot functions for effective assessment of case influence in complicated models. Lastly, it supports multiple-group models and the handling of missing data. This manuscript demonstrates how to utilize semfindr for efficient search for influential cases, providing publication-ready results and plots.
Treatment Effect Moderation with Small Subgroups: An Incremental Subgroup Analysis Approach.
Liu X, Eddy JM, Martinez CR
Multivariate Behav Res · 2026 Mar · PMID 41770547 · Publisher ↗
Subgroup analysis is an important tool for studying treatment effect moderation. However, when a subgroup has a relatively small proportion (referred to as "focal subgroup"), standard subgroup analysis could encounter pr...
Subgroup analysis is an important tool for studying treatment effect moderation. However, when a subgroup has a relatively small proportion (referred to as "focal subgroup"), standard subgroup analysis could encounter practical difficulties (e.g., low estimation precision). In this study, we propose an incremental subgroup analysis approach, which considers how the treatment effect would change as the proportion of focal subgroup gradually increases. The proposed approach provides estimates and confidence intervals for incremental subgroup effects, allowing visualization of the effect moderation trend with a continuous curve along with the corresponding confidence band. For estimation with baseline covariates, we extend a doubly robust method that can incorporate machine learning approaches for relaxing modeling assumptions, while allowing quantification of uncertainty for the effect estimate (e.g., via confidence intervals). Simulations are conducted to evaluate the performance of the estimation method. We illustrate the application of the proposed approach in an empirical example, assessing the moderation in the effect of a preventive intervention based on a relatively small subgroup. We hope that the proposed subgroup analysis approach provides an alternative or complementary method for studying effect moderation by subgroups.
Penalized Subgrouping of Heterogeneous Time Series.
Crawford CM, Park JJ, Chow SM … +3 more , Ernst AF, Pipiras V, Fisher ZF
Multivariate Behav Res · 2026 Feb · PMID 41718445 · Publisher ↗
Interest in the study and analysis of dynamic processes in the social, behavioral, and health sciences has burgeoned in recent years due to the increased availability of intensive longitudinal data. However, how best to...
Interest in the study and analysis of dynamic processes in the social, behavioral, and health sciences has burgeoned in recent years due to the increased availability of intensive longitudinal data. However, how best to model and account for the persistent heterogeneity characterizing such processes remains an open question. The multi-VAR framework, a recent methodological development built on the vector autoregressive model, accommodates heterogeneous dynamics in multiple-subject time series through structured penalization. In the original multi-VAR proposal, individual-level transition matrices are decomposed into common and unique dynamics, allowing for generalizable and person-specific features. The current project extends this framework to allow additionally for the identification and penalized estimation of subgroup-specific dynamics; that is, patterns of dynamics that are shared across subsets of individuals. The performance of the proposed subgrouping extension is evaluated in the context of both a simulation study and empirical application, and results are compared to alternative methods for subgrouping multiple-subject, multivariate time series.
Calculating and Interpreting Maximal Reliability in Bifactor Models.
Li S, Savalei V
Multivariate Behav Res · 2026 · PMID 41637133 · Publisher ↗
Confirmatory bifactor models have been widely applied to understand multidimensional constructs in different areas of psychology research. Maximal reliability captures how well an optimal linear composite (OLC) represent...
Confirmatory bifactor models have been widely applied to understand multidimensional constructs in different areas of psychology research. Maximal reliability captures how well an optimal linear composite (OLC) represents the target latent variable. In this article, we point out that researchers have been using an incorrect generalization of coefficient H, a maximal reliability coefficient developed for one-factor models, with bifactor models. We present two sets of correct equations for maximal reliability: one based on an OLC for the entire scale and one based on a sub-composite consisting only of relevant items (OLSC). We illustrate these equations on a simulated data example and on a real data example, and compare them to other reliability coefficients. In a small population simulation, we find that OLCs and OLSCs are not reliable measures of group factors in models that contain fewer than 100 indicators. In addition, somewhat unexpectedly, we find that OLCs and OLSCs often receive negative weights. Overall, we recommend against using optimal composites or sub-composites as proxies for group factors, due to poor reliability and difficulties of interpretation. However, maximal reliability indices can be reported to evaluate the quality of a bifactor model.
Multiple Imputation of Missing Data in Moderated Factor Analysis.
van Ginkel JR, Molenaar D
Multivariate Behav Res · 2026 · PMID 41575264 · Publisher ↗
In moderated factor analysis, the parameters of the traditional common factor model are a function of an external continuous moderator variable. Handling missing values on the observed indicator variables of the common f...
In moderated factor analysis, the parameters of the traditional common factor model are a function of an external continuous moderator variable. Handling missing values on the observed indicator variables of the common factors is straightforward as the parameters can be estimated using full information maximum likelihood. However, for cases with missing values on the moderator variable the likelihood function cannot be evaluated. Consequently, in practical applications of the moderated factor model, these cases are omitted from the analysis by listwise deletion. As listwise deletion is known to potentially affect the consistency and precision of the results, we propose a moderated factor model based multiple imputation procedure for handling missing values on the moderator variable in the presence of missing values on the indicator variables. We compare this new procedure with listwise deletion and predictive mean matching. The results show that both listwise deletion and predictive mean matching have less power and produce more bias in parameter estimates than multiple imputation under the moderated factor model.
Time-Varying Path-Specific Direct and Indirect Effects: A Novel Approach to Examine Dynamic Behavioral Processes with Application to Smoking Cessation.
Chakraborti Y, M Yucel R, Piper ME … +4 more , Mennis J, Alberg AJ, B Baker T, Coffman DL
Multivariate Behav Res · 2026 Jan · PMID 41556314 · Publisher ↗
Behavioral processes are often complex, and vary over time, requiring intensive longitudinal data to effectively capture the dynamic elements involved. For example, examining daily socio-behavioral and treatment adherenc...
Behavioral processes are often complex, and vary over time, requiring intensive longitudinal data to effectively capture the dynamic elements involved. For example, examining daily socio-behavioral and treatment adherence data collected during a smoking quit attempt, can reveal how, when, and why withdrawal symptoms change, offering insight into critical windows of relapse-risk in the cessation process. However, analytical methods (e.g., time-varying causal mediation methods), that can translate such intensive longitudinal data into time-varying causal effects remain limited, hindering a deeper understanding of these dynamic behavioral processes. We propose a new approach, augmented mediational g-formula with a two-step estimation strategy, to estimate time-varying causal (in)direct effects. Its performance was evaluated simulation, comparing bias, precision, and alignment with the product-of-coefficients approach. The optimal approach identified by the simulation study was applied to data from the Wisconsin Smokers' Health Study II, for assessing the effect of randomized pharmacological treatment assignment (exposure) on daily smoking cessation outcome(s), mediated daily treatment adherence, in the presence of a time-varying confounder (daily stress). Daily stress was due to social contextual factors but not affected by the exposure. Within its scope, this study serves as a preliminary framework for studying the causal structure of time-varying bio-behavioral processes.
Moderating the Consequences of Longitudinal Change for Distal Outcomes.
McCormick EM
Multivariate Behav Res · 2026 Jan · PMID 41532470 · Publisher ↗
There has been a growing interest in using earlier change to predict downstream distal outcomes in development; however, prior work has mostly focused on estimating the unique effect of the different growth parameters (e...
There has been a growing interest in using earlier change to predict downstream distal outcomes in development; however, prior work has mostly focused on estimating the unique effect of the different growth parameters (e.g., intercept and slope) rather than focusing on the trajectory as a whole. Here I lay out a distal outcome latent curve model with latent interactions which attempts to model the effect of growth parameters on these later outcomes. I show again that these models require us to contend with unintuitive time coding effects which can impact the direction and significance of effects and that plotting and probing are necessary for disambiguating these joint effects. These graphical approaches emphasize practical steps for applied researchers in understanding these effects. I then outline how future research can help clarify optimal approaches for using the trajectory as a whole rather than the unique effects of its individual sub-components.
A Latent Space Graded Response Model for Likert-Scale Psychological Assessments.
De Carolis L, Kang I, Jeon M
Multivariate Behav Res · 2026 · PMID 41467616 · Publisher ↗
In this study, we introduce a novel modeling approach for ordinal response data, extending the one-parameter graded response model. The proposed model incorporates unobserved interactions between respondents and items, r...
In this study, we introduce a novel modeling approach for ordinal response data, extending the one-parameter graded response model. The proposed model incorporates unobserved interactions between respondents and items, represented as distances in a two-dimensional Euclidean space, referred to as an interaction map. This latent space graded response model (LSGRM) addresses potential violations of the conditional independence assumption shared by traditional main-effect-only psychometric models and offers a visualization tool for exploring conditional dependence in ordinal item response data. Through simulation and empirical studies, we illustrate the utility of the proposed approach in analyzing Likert-scale psychological assessment data. Also, by comparing the results with those from other models of different data modalities, we examined the impact of dichotomization and treating ordinal responses as continuous on conditional dependence.
A Two-Step Robust Estimation Approach for Inferring Within-Person Relations in Longitudinal Design: Tutorial and Simulations.
Usami S
Multivariate Behav Res · 2026 · PMID 41454737 · Publisher ↗
Psychological researchers have shown an interest in disaggregating within-person variability from between-person differences. This paper provides a tutorial, simulation, and illustrative example of a new approach propose...
Psychological researchers have shown an interest in disaggregating within-person variability from between-person differences. This paper provides a tutorial, simulation, and illustrative example of a new approach proposed by Usami (2023). This approach consists of a two-step procedure: (WPVS) for each person, which are disaggregated from the stable traits of that person, are predicted using structural equation modeling, and causal parameters are then estimated a potential outcome approach, such as by using structural nested mean models (SNMMs). This method has several advantages: (i) the flexible inclusion of curvilinear and interaction effects for WPVS as latent variables in treatment and outcome models, (ii) more accurate estimates of causal parameters for reciprocal relations can be obtained under certain conditions owing to them being doubly robust, even if unobserved time-varying confounders and model misspecifications exist, (iii) no models for (the distributions of) observed time-varying confounders are needed for estimation, and (iv) the risk of obtaining improper solutions is reduced. Estimation performances are investigated through large-scale simulations and it shows that the proposed approach works well in many conditions if longitudinal data with are available. An analytic example using data from the Tokyo Teen Cohort (TTC) study is also provided.
Neural Network Analysis of Psychological Data: A Step-by-Step Guide.
Tong L, Zhang Z
Multivariate Behav Res · 2026 · PMID 41332415 · Publisher ↗
Artificial neural networks (ANN) have attracted increasing attention in the field of psychology. With the availability of software programs, the wide application of ANN becomes possible. However, without a firm understan...
Artificial neural networks (ANN) have attracted increasing attention in the field of psychology. With the availability of software programs, the wide application of ANN becomes possible. However, without a firm understanding of the basics of the ANN, issues can easily arise. This article presents a step-by-step guide for implementing a feed-forward neural network (FNN) on a psychological data set to illustrate the critical steps in building, estimating, and interpreting a neural network model. We start with a concrete example of a basic 3-layer FNN, illustrating the core concepts, the matrix representation, and the whole optimization process. By adjusting parameters and changing the model structure, we examine their effects on model performance. Then, we introduce accessible methods for interpreting model results and making inferences. Through the guide, we hope to help researchers avoid common problems in applying neural network models and machine learning methods in general.
Novel Full-Bayesian and Hybrid-Bayesian Approaches for Modeling Intraindividual Variability.
Fang Y, Wang L
Multivariate Behav Res · 2026 · PMID 41328730 · Publisher ↗
Intraindividual variability (IIV) characterizes the amplitude and temporal dependency of short-term fluctuations of a variable and is often used to predict outcomes in psychological studies. However, how to properly mode...
Intraindividual variability (IIV) characterizes the amplitude and temporal dependency of short-term fluctuations of a variable and is often used to predict outcomes in psychological studies. However, how to properly model IIV is understudied. In particular, intraindividual standard deviation (or variance), which quantifies the amplitude of fluctuation of a variable around its mean level, can be challenging to model directly in popular latent variable frameworks, such as dynamic structural equation modeling (DSEM). In this study, we introduced three novel modeling methods, including two two-step hybrid-Bayesian methods using DSEM and a one-step full Bayesian method, to model IIV as predictors. We conducted a simulation study to evaluate the performance of the three methods and compared their performance to that of the conventional regression approach under various data conditions. Simulation results showed that the hybrid-Bayesian approach with multiple draws (HBM) and the one-step full Bayesian (FB) approach performed well in recovering the parameters when sufficient sample size and time points were available. The data requirement of using FB was lower than HBM. However, the conventional approach and hybrid-Bayesian approach with a single draw failed to recover parameters, even with large samples. We provided a simulated data example with code online to illustrate the use of the methods.
Integrated Trend and Lagged Modeling of Multi-Subject, Multilevel, and Short Time Series.
Xiong X, Li Y, Hunter MD … +1 more , Chow SM
Multivariate Behav Res · 2026 · PMID 41273071 · Publisher ↗
Trends represent systematic intra-individual variations that occur over slower time scales that, if unaccounted, are known to yield biases in estimation of momentary change patterns captured by time series models. The ap...
Trends represent systematic intra-individual variations that occur over slower time scales that, if unaccounted, are known to yield biases in estimation of momentary change patterns captured by time series models. The applicability of detrending methods has rarely been assessed in the context of multi-level longitudinal panel data, namely, nested data structures with relatively few measurements. This paper evaluated the efficacy of a series of two-stage detrending methods against a single-stage Bayesian approach in fitting ulti-evel nonlinear rowth curve models with utoegressive residuals (ml-GAR) with random effects in both the growth and autoregressive processes. Monte Carlo simulation studies revealed that the single-stage Bayesian approach, in contrast to two-stage approaches, exhibited satisfactory properties with as few as five time points when the number of individuals was large (e.g., 500 individuals). It still outperformed alternative two-stage approaches when correlated random effects between the trend and autoregressive processes were misspecified as a diagonal random effect structure. Empirical results from the Early Childhood Longitudinal Study-Kindergarten Class (ECLS-K) data suggested substantial deviations in conclusions regarding children's reading ability using two-stage in comparison to single-stage approaches, thus highlighting the importance of simultaneous modeling of trends and intraindividual variability whenever feasible.
Demystifying Posterior Distributions: A Tutorial on Their Derivation.
Du H, Liu F, Zhang Z … +1 more , Enders C
Multivariate Behav Res · 2026 · PMID 41273045 · Publisher ↗
Bayesian statistics have gained significant traction across various fields over the past few decades. Bayesian statistics textbooks often provide both code and the analytical forms of parameters for simple models. Howeve...
Bayesian statistics have gained significant traction across various fields over the past few decades. Bayesian statistics textbooks often provide both code and the analytical forms of parameters for simple models. However, they often omit the process of deriving posterior distributions or limit it to basic univariate examples focused on the mean and variance. Additionally, these resources frequently assume a strong background in linear algebra and probability theory, which can present barriers for researchers without extensive mathematical training. This tutorial aims to fill that gap by offering a step-by-step guide to deriving posterior distributions. We aim to make concepts typically reserved for advanced statistics courses more accessible and practical. This tutorial will cover two models: the univariate normal model and the multilevel model. The concepts and properties demonstrated in the two examples can be generalized to other models and distributions.
Regression Discontinuity Analysis with Latent Variables.
Morell M, Kwon M, Han Y … +3 more , Sung Y, Liu Y, Yang JS
Multivariate Behav Res · 2026 · PMID 41273024 · Publisher ↗
A regression discontinuity (RD) design is often employed to provide causal evidence when the randomization of the treatment assignment is infeasible. When variables of interest are latent constructs measured by observed...
A regression discontinuity (RD) design is often employed to provide causal evidence when the randomization of the treatment assignment is infeasible. When variables of interest are latent constructs measured by observed indicators, the conventional RD analysis using observed variable scores does not allow researchers to examine heterogeneity in the estimated local average treatment effect (ATE) and to generalize the ATE to participants away from the cutoff. We propose a novel methodological augmentation to the conventional RD analysis, which assumes the availability of multiple indicator variables (i.e., raw item responses) that measure the latent construct underlying the running variable. By specifying an explicit measurement model based on those indicator variables, our latent RD framework allows 1) defining the local ATE conditional on the latent construct, 2) disentangling the heterogeneity of the local ATE, and 3) generalizing the local ATE to running variable scores away from the cutoff. In a proof-of-concept simulation we illustrate the proposed augmentation recovers parameters of interest well under practical test length and sample size conditions.
Targeted Maximum Likelihood Estimation for Causal Inference With Observational Data-The Example of Private Tutoring.
Jindra C, Sachse KA
Multivariate Behav Res · 2026 · PMID 41267548 · Publisher ↗
State-of-the-art causal inference methods for observational data promise to relax assumptions threatening valid causal inference. Targeted maximum likelihood estimation (TMLE), for example, is a template for constructing...
State-of-the-art causal inference methods for observational data promise to relax assumptions threatening valid causal inference. Targeted maximum likelihood estimation (TMLE), for example, is a template for constructing doubly robust, semiparametric, efficient substitution estimators, providing consistent estimates if the outcome or treatment model is correctly specified. Compared to standard approaches, it reduces the risk of misspecification bias by allowing (nonparametric) machine-learning techniques, including super learning, to estimate the relevant components of the data distribution. We briefly introduce TMLE and demonstrate its use by estimating the effects of private tutoring in mathematics during Year 7 on mathematics proficiency and grades using observational data from starting cohort 3 of the National Education Panel Study ( 4,167). We contrast TMLE estimates to those from ordinary least squares, the parametric G-formula, and the augmented inverse-probability weighted estimator. Our findings reveal close agreement between methods for end-of-year grades. However, variations emerge when examining mathematics proficiency as the outcome, highlighting that substantive conclusions may depend on the analytical approach. The results underscore the significance of employing advanced causal inference methods, such as TMLE, when navigating the complexities of observational data and highlight the nuanced impact of methodological choices on the interpretation of study outcomes.
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