Bengt Muthén
Biographic Data
| ID | 267265 |
|---|---|
| NAME | Bengt Muthén |
| GIVEN NAMES | Bengt |
| FAMILY NAME | Muthén |
| SIGNATURE | MUTHÉN B |
| AFFILIATIONS | University of California, Los Angeles |
| ORCID | 0000-0001-9308-6525 |
| VERIFIED | Yes |
| TOTAL WORKS | 59 |
| TOTAL CITATIONS | 490 |
| AUTHOR COUNT | 59 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1977 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 7 |
A Unification of Second-Order and Bi-Factor EFA
As empirical applications and methodological research on second-order exploratory factor analysis have matured, important refinements to estimation procedures, interpretive frameworks, and theoretical expectations have emerged. These advances establish second-order EFA as a rigorous alternative to bi-factor EFA and to conventional EFA models characterized by substantial factor correlations. We further demonstrate that bi-factor EFA models constit…
Three-Level Dynamic Structural Equation Modeling
In this paper, we describe a three level dynamic structural modeling framework as a generalization of the DSEM framework of Asparouhov et al. Model estimation is discussed and the framework is illustrated with simulation studies and practical examples. Two common scenarios are described. The first is intensive longitudinal data for a group of individuals where observations are nested within days, periods, waves or bursts. The second is intensive …
Penalized Structural Equation Models
Penalized structural equation models (PSEM) is a new powerful estimation technique that can be used to tackle a variety of difficult structural estimation problems that can not be handled with previously developed methods. In this paper we describe the PSEM framework and illustrate the quality of the method with simulation studies. Maximum-likelihood and weighted least squares PSEM estimation is discussed for SEM models with continuous and catego…
Methodological Advances with Penalized Structural Equation Models
Dynamic Structural Equation Modeling with Cycles
Multiple Group Alignment for Exploratory and Structural Equation Models
The multiple group alignment methodology is adapted to the general structural equation model. This includes models with cross-loadings, covariates, and structural relations among the factors. A group-specific model for the factors can be estimated even when measurement invariance does not hold, including groups-specific factor means, intercepts, and variances. The methodology is also extended to the weighted least squares estimation method to acc…
Residual Structural Equation Models
The residual variables in a structural equation model can be used to create a secondary structural model which we call the residual structural equation model (RSEM). We describe the maximum-likelihood, weighted least squares and Bayesian estimations for RSEM. The methodology is illustrated with several examples and simulation studies. We discuss the implementation of RSEM in the Mplus software package and provide scripts for the simulation studie…
Why Measurement Invariance is Important in Comparative Research. A Response to Welzel et al. (2021)
Welzel et al. (2021) claim that non-invariance of instruments is inconclusive and inconsequential in the field for cross-cultural value measurement. In this response, we contend that several key arguments on which Welzel et al. (2021) base their critique of invariance testing are conceptually and statistically incorrect. First, Welzel et al. (2021) claim that value measurement follows a formative rather than reflective logic. Yet they do not prov…
Measurement invariance in the social sciences: Historical development, methodological challenges, state of the art, and future perspectives
Expanding the Bayesian structural equation, multilevel and mixture models to logit, negative-binomial, and nominal variables
Recent work on the Polya-Gamma distribution provides a breakthrough for the Bayesian modeling of logit, count, and nominal variables. We describe how the methodology is incorporated in the Mplus modeling framework and illustrate it with several examples: logistic latent growth models, multilevel IRT, multilevel time-series models for count data, multilevel nominal regression, and nominal factor analysis
Advances in Bayesian Model Fit Evaluation for Structural Equation Models
In this article, we discuss the Posterior Predictive P-value (PPP) method in the presence of missing data, the Bayesian adaptation of the approximate fit indices RMSEA, CFI and TLI, as well as the Bayesian adaptation of the Wald test for nested models. Simulation studies are presented. We also illustrate how these new methods can be used to build BSEM models
Bayesian estimation of single and multilevel models with latent variable interactions
In this article, we discuss single and multilevel SEM models with latent variable interactions. We describe the Bayesian estimation for these models and show through simulation studies that the Bayesian method outperforms other methods such as the maximum-likelihood method. We show that multilevel moderation models can easily be estimated with the Bayesian method
The fixed versus random effects debate and how it relates to centering in multilevel modeling.
In many disciplines researchers use longitudinal panel data to investigate the potentially causal relationship between 2 variables. However, the conventions and concerns vary widely across disciplines. Here we focus on 2 concerns, that is: (a) the concern about random effects versus fixed effects, which is central in the (micro)econometrics/sociology literature; and (b) the concern about grand mean versus group (or person) mean centering, which i…
Latent Variable Centering of Predictors and Mediators in Multilevel and Time-Series Models
In hierarchical linear regression models the question regarding the proper way to construct covariates has long been the focus of attention. The main issue is whether or not the covariates should b...
What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups.
Scalar invariance is an unachievable ideal that in practice can only be approximated; often using potentially questionable approaches such as partial invariance based on a stepwise selection of parameter estimates with large modification indices. Study 1 demonstrates an extension of the power and flexibility of the alignment approach for comparing latent factor means in large-scale studies (30 OECD countries, 8 factors, 44 items, N = 249,840), fo…
Number of Subjects and Time Points Needed for Multilevel Time-Series Analysis: A Simulation Study of Dynamic Structural Equation Modeling
Dynamic structural equation modeling (DSEM) is a novel, intensive longitudinal data (ILD) analysis framework. DSEM models intraindividual changes over time on Level 1 and allows the parameters of these processes to vary across individuals on Level 2 using random effects. DSEM merges time series, structural equation, multilevel, and time-varying effects models. Despite the well-known properties of these analysis areas by themselves, it is unclear …
At the Frontiers of Modeling Intensive Longitudinal Data: Dynamic Structural Equation Models for the Affective Measurements from the Cogito Study
With the growing popularity of intensive longitudinal research, the modeling techniques and software options for such data are also expanding rapidly. Here we use dynamic multilevel modeling, as it is incorporated in the new dynamic structural equation modeling (DSEM) toolbox in Mplus, to analyze the affective data from the COGITO study. These data consist of two samples of over 100 individuals each who were measured for about 100 days. We use co…
Recent Methods for the Study of Measurement Invariance With Many Groups: Alignment and Random Effects
This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close t…
Measurement Invariance in Cross-National Studies: Challenging Traditional Approaches and Evaluating New Ones
Bayesian Structural Equation Modeling With Cross-Loadings and Residual Covariances: Comments on Stromeyer et al.
A recent article in the Journal of Management gives a critique of a Bayesian approach to factor analysis proposed in Psychological Methods. This commentary responds to the authors’ critique by clarifying key issues, especially the use of priors for residual covariances. A discussion is also presented of cross-loadings and model selection tools. Simulated data are used to illustrate the ideas. A reanalysis of the example used by the authors reveal…
Causal Effects in Mediation Modeling: An Introduction With Applications to Latent Variables
Causal inference in mediation analysis offers counterfactually based causal definitions of direct and indirect effects, drawing on research by Robins, Greenland, Pearl, VanderWeele, Vansteelandt, Imai, and others. This type of mediation effect estimation is little known and seldom used among analysts using structural equation modeling (SEM). The aim of this article is to describe the new analysis opportunities in a way that is accessible to SEM a…
Multiple-Group Factor Analysis Alignment
This article presents a new method for multiple-group confirmatory factor analysis (CFA), referred to as the alignment method. The alignment method can be used to estimate group-specific factor means and variances without requiring exact measurement invariance. A strength of the method is the ability to conveniently estimate models for many groups. The method is a valuable alternative to the currently used multiple-group CFA methods for studying …
Auxiliary Variables in Mixture Modeling: Three-Step Approaches Using M plus
This article discusses alternatives to single-step mixture modeling. A 3-step method for latent class predictor variables is studied in several different settings, including latent class analysis, latent transition analysis, and growth mixture modeling. It is explored under violations of its assumptions such as with direct effects from predictors to latent class indicators. The 3-step method is also considered for distal variables. The Lanza, Tan…
Facing off with Scylla and Charybdis: A comparison of scalar, partial, and the novel possibility of approximate measurement invariance
Measurement invariance (MI) is a pre-requisite for comparing latent variable scores across groups. The current paper introduces the concept of approximate MI building on the work of Muthén and Asparouhov and their application of Bayesian Structural Equation Modeling (BSEM) in the software Mplus. They showed that with BSEM exact zeros constraints can be replaced with approximate zeros to allow for minimal steps away from strict MI, still yielding …
Bayesian structural equation modeling: A more flexible representation of substantive theory.
This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventio…
Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance
Addresses issues related to partial measurement in variance using a tutorial approach based on the LISREL confirmatory factor analytic model. Specifically, we demonstrate procedures for (a) using "sensitivity analyses " to establish stable and substantively well-fitting baseline models, (b) determining partially invariant measurement parameters, and (c) testing for the invariance of factor covariance and mean structures, given partial measurement…
Complex Sample Data in Structural Equation Modeling
Large-scale surveys using complex sample designs are frequently carried out by government agencies. The statistical analysis technology available for such data is, however, limited in scope. This study investigates and further develops statistical methods that could be used in software for the analysis of data collected under complex sample designs. First, it identifies several recent methodological lines of inquiry which taken together provide a…
Assessing Reliability and Stability in Panel Models
Latent Variable Modeling of Longitudinal and Multilevel Data
An overview is given of modeling of longitudinal and multilevel data using a latent variable framework. Particular emphasis is placed on growth modeling. A latent variable model is presented for three-level data, where the modeling of the longitudinal part of the data imposes both a covariance and a mean structure. Examples are discussed where repeated observations are made on students sampled within classrooms and schools
Measurement invariance in the social sciences: Historical development, methodological challenges, state of the art, and future perspectives
Recent Methods for the Study of Measurement Invariance With Many Groups: Alignment and Random Effects
This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close t…
The Application of Latent Curve Analysis to Testing Developmental Theories in Intervention Research
The effectiveness of a prevention or intervention program has traditionally been assessed using time‐specific comparisons of mean levels between the treatment and the control groups. However, many times the behavior targeted by the intervention is naturally developing over time, and the goal of the treatment is to alter this natural or normative developmental trajectory. Examining time‐specific mean levels can be both limiting and potentially mis…
Dichotomous Factor Analysis of Symptom Data
This article discusses how a factor model with continuous latent variables can be used to analyze a set of strongly skewed dichotomous items and how such a model can be used for classification of subjects. The suitability of the specification of normally distributed latent variables, as is assumed with the use of tetrachoric correlations, is investigated. Both exploratory and confirmatory analyses, including multiple groups with mean structures, …
Measurement Invariance in Cross-National Studies: Challenging Traditional Approaches and Evaluating New Ones
Dynamic Structural Equation Modeling with Cycles
Assessing Reliability and Stability in Panel Models
Measuring Religious Attitudes Using the Semantic Differential Technique: An Application of Three-Mode Factor Analysis
Ulf Olsson, Thorleif Pettersson, Gustaf Stahlberg, Measuring Religious Attitudes Using the Semantic Differential Technique: An Application of Three-Mode Factor Analysis, Journal for the Scientific Study of Religion, Vol. 16, No. 3 (Sep., 1977), pp. 275-288
Contributions to Factor Analysis of Dichotomous Variables
A new method is proposed for the factor analysis of dichotomous variables. Similar to the method of Christoffersson this uses information from the first and second order proportions to fit a multiple factor model. Through a transformation into a new set of sample characteristics, the estimation is considerably simplified. A generalized least-squares estimator is proposed, which asymptotically is as efficient as the corresponding estimator of Chri…
Latent variable structural equation modeling with categorical data
A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators
A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator model…
A comparison of some methodologies for the factor analysis of non‐normal Likert variables
This paper considers the problem of applying factor analysis to non‐normal categorical variables. A Monte Carlo study is conducted where five prototypical cases of non‐normal variables are generated. Two normal theory estimators, ML and GLS, are compared to Browne's (1982) ADF estimator. A categorical variable methodology (CVM) estimator of Muthén (1984) is also considered for the most severely skewed case. Results show that ML and GLS chi‐square…
On Structural Equation Modeling with Data that are not Missing Completely at Random
A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connec…
Latent Variable Modeling in Heterogeneous Populations
Common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values. This article describes the problem and gives an overview of methodology that can address heterogeneity. Artificial examples of mixtures are given, where if the mixture is not recognized, strongly distorted results occur. MIMIC structural modeling is shown to be a useful method for detecting …
Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance
Addresses issues related to partial measurement in variance using a tutorial approach based on the LISREL confirmatory factor analytic model. Specifically, we demonstrate procedures for (a) using "sensitivity analyses " to establish stable and substantively well-fitting baseline models, (b) determining partially invariant measurement parameters, and (c) testing for the invariance of factor covariance and mean structures, given partial measurement…
Dichotomous Factor Analysis of Symptom Data
This article discusses how a factor model with continuous latent variables can be used to analyze a set of strongly skewed dichotomous items and how such a model can be used for classification of subjects. The suitability of the specification of normally distributed latent variables, as is assumed with the use of tetrachoric correlations, is investigated. Both exploratory and confirmatory analyses, including multiple groups with mean structures, …
A comparison of some methodologies for the factor analysis of non‐normal Likert variables: A note on the size of the model
This paper expands on a recent study by Muthen & Kaplan (1985) by examining the impact of non‐normal Likert variables on testing and estimation in factor analysis for models of various size. Normal theory GLS and the recently developed ADF estimator are compared for six cases of non‐normality, two sample sizes, and four models of increasing size in a Monte Carlo framework with a large number of replications. Results show that GLS and ADF chi‐squa…
Complex Sample Data in Structural Equation Modeling
Large-scale surveys using complex sample designs are frequently carried out by government agencies. The statistical analysis technology available for such data is, however, limited in scope. This study investigates and further develops statistical methods that could be used in software for the analysis of data collected under complex sample designs. First, it identifies several recent methodological lines of inquiry which taken together provide a…
General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation.
The generality of latent variable modeling of individual differences in development over time is demonstrated with a particular emphasis on randomized intervention studies. First, a brief overview is given of biostatistica l and psychometric approaches to repeated measures analysis. Second, the generality of the psychometric approach is indicated by some nonstandard models. Third, a multiple-population analysis approach is proposed for the estima…
Latent Variable Modeling of Longitudinal and Multilevel Substance Use Data
This article demonstrates the use of a general model for latent variable growth analysis which takes into account cluster sampling. Multilevel Latent Growth Modeling (MLGR4) was used to analyze longitudinal and multilevel data for adolescent and parent substance use measured at four annual time points. An associative LGM model was tested for alcohol, marijuana, and cigarette use with a sample of 435 families. Hypotheses concerning the shape of th…
Latent Variable Modeling of Longitudinal and Multilevel Data
An overview is given of modeling of longitudinal and multilevel data using a latent variable framework. Particular emphasis is placed on growth modeling. A latent variable model is presented for three-level data, where the modeling of the longitudinal part of the data imposes both a covariance and a mean structure. Examples are discussed where repeated observations are made on students sampled within classrooms and schools
Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm
This paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables. The research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome. More generally, this model …
The Application of Latent Curve Analysis to Testing Developmental Theories in Intervention Research
The effectiveness of a prevention or intervention program has traditionally been assessed using time‐specific comparisons of mean levels between the treatment and the control groups. However, many times the behavior targeted by the intervention is naturally developing over time, and the goal of the treatment is to alter this natural or normative developmental trajectory. Examining time‐specific mean levels can be both limiting and potentially mis…
The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample.
OBJECTIVE: The purpose of this study is to add to the understanding of the development of heavy alcohol use and alcohol-related problems by examining data from the National Longitudinal Survey of Youth (NLSY), a general population sample that contains information on alcohol use for the ages 18-37. A key question in this study is how background characteristics of the individual influence this development and whether the influence of these backgrou…
Integrating Person‐Centered and Variable‐Centered Analyses: Growth Mixture Modeling With Latent Trajectory Classes
Background: Many alcohol research questions require methods that take a person‐centered approach because the interest is in finding heterogeneous groups of individuals, such as those who are susceptible to alcohol dependence and those who are not. A person‐centered focus also is useful with longitudinal data to represent heterogeneity in developmental trajectories. In alcohol, drug, and mental health research the recognition of heterogeneity has …
How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power
A common question asked by researchers is, "What sample size do I need for my study?" Over the years, several rules of thumb have been proposed. In reality there is no rule of thumb that applies to all situations. The sample size needed for a study depends on many factors, including the size of the model, distribution of the variables, amount of missing data, reliability of the variables, and strength of the relations among the variables. The pur…
Beyond SEM: General Latent Variable Modeling
Statistical and Substantive Checking in Growth Mixture Modeling: Comment on Bauer and Curran (2003).
This commentary discusses the D. J. Bauer and P. J. Curran (2003) investigation of growth mixture modeling. Single-class modeling of nonnormal outcomes is compared with modeling with multiple latent trajectory classes. New statistical tests of multiple-class models are discussed. Principles for substantive investigation of growth mixture model results are presented and illustrated by an example of high school dropout predicted by low mathematics …
Applying Multigroup Confirmatory Factor Models for Continuous Outcomes to Likert Scale Data Complicates Meaningful Group Comparisons
Treating Likert rating scale data as continuous outcomes in confirmatory factor analysis violates the assumption of multivariate normality. Given certain requirements pertaining to the number of categories, skewness, size of the factor loadings, and so forth, it seems nevertheless possible to recover true parameter values if the data stem from a single homogeneous population. It is shown that, in a multigroup context, an analysis of Likert data u…
Latent Variable Analysis: Growth Mixture Modeling and Related Techniques for Longitudinal Data
This chapter gives an overview of recent advances in latent variable analysis. Emphasis is placed on the strength of modeling obtained by using a flexible combination of continuous and categorical latent variables.
Investigating population heterogeneity with factor mixture models.
Sources of population heterogeneity may or may not be observed. If the sources of heterogeneity are observed (e.g., gender), the sample can be split into groups and the data analyzed with methods for multiple groups. If the sources of population heterogeneity are unobserved, the data can be analyzed with latent class models. Factor mixture models are a combination of latent class and common factor models and can be used to explore unobserved popu…
Mathematics (53 works) · Statistics (50 works) · Econometrics (48 works) · Structural equation modeling (43 works) · Computer Science (41 works) · Psychology (25 works) · Latent variable (24 works) · Psychometric Methodologies and Testing (21 works) · Advanced Statistical Modeling Techniques (17 works) · Confirmatory factor analysis (15 works)