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Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling 14
, 2007
"... Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models ’ usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deci ..."
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Cited by 177 (7 self)
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Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models ’ usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study population. This article presents the results of a simulation study that examines the performance of likelihoodbased tests and the traditionally used Information Criterion (ICs) used for determining the number of classes in mixture modeling. We look at the performance of these tests and indexes for 3 types of mixture models: latent class analysis (LCA), a factor mixture model (FMA), and a growth mixture models (GMM). We evaluate the ability of the tests and indexes to correctly identify the number of classes at three different sample sizes (n D 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test proved to be a very consistent indicator of classes across all of the models considered.
Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood? Multivariate Behavioral Research
 Multivariate Behavioral Research
, 2006
"... Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an und ..."
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Cited by 27 (4 self)
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Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or categorical, and (b) to quantify the effect of sample size and class proportions on making this distinction. Latent variable models with categorical, continuous, or both types of latent variables are fitted to simulated data generated under different types of latent variable models. If an analysis is restricted to fitting continuous latent variable models assuming a homogeneous population and data stem from a heterogeneous population, overextraction of factors may occur. Similarly, if an analysis is restricted to fitting latent class models, overextraction of classes may occur if covariation between observed variables is due to continuous factors. For the datagenerating models used in this study, comparing the fit of different exploratory factor mixture models usually allows one to distinguish correctly between categorical and/or continuous latent variables. Correct model choice depends on class separation and withinclass sample size. Starting with the introduction of factor analysis by Spearman (1904), different types of latent variable models have been developed in various areas of the social sciences. Apart from proposed estimation methods, the most obvious differences between these early latent variable models concern the assumed distribution of the Correspondence concerning this article should be addressed to Gitta H. Lubke, Department of Psychology,
Performance of factor mixture models as a function of model size, covariate effects, and classspecific parameters. Structural Equation Modeling
, 2007
"... Factor mixture models are designed for the analysis of multivariate data obtained from a population consisting of distinct latent classes. A common factor model is assumed to hold within each of the latent classes. Factor mixture modeling involves obtaining estimates of the model parameters, and may ..."
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Cited by 24 (2 self)
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Factor mixture models are designed for the analysis of multivariate data obtained from a population consisting of distinct latent classes. A common factor model is assumed to hold within each of the latent classes. Factor mixture modeling involves obtaining estimates of the model parameters, and may also be used to assign subjects to their most likely latent class. This simulation study investigates aspects of model performance such as parameter coverage and correct class membership assignment and focuses on covariate effects, model size, and classspecific versus classinvariant parameters. When fitting true models, parameter coverage is good for most parameters even for the smallest class separation investigated in this study (0.5 SD between 2 classes). The same holds for convergence rates. Correct class assignment is unsatisfactory for the small class separation without covariates, but improves dramatically with increasing separation, covariate effects, or both. Model performance is not influenced by the differences in model size investigated here. Classspecific parameters may improve some aspects of model performance but negatively affect other aspects. Factor mixture models combine latent class analysis and common factor analysis. Factor mixture models are designed for data from possibly heterogenous populations consisting of several latent classes, and are an adequate choice if it is reasonable to assume that observed variables within each class can be modeled using a common factor model. There are two types of latent variables in factor mixture
A model for integrating fixed, random, and mixedeffects metaanalyses into structural equation modeling
 Psychological Methods
, 2008
"... Metaanalysis and structural equation modeling (SEM) are two important statistical methods in the behavioral, social, and medical sciences. They are generally treated as two unrelated topics in the literature. The present article proposes a model to integrate fixed, random, and mixedeffects meta ..."
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Cited by 12 (1 self)
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Metaanalysis and structural equation modeling (SEM) are two important statistical methods in the behavioral, social, and medical sciences. They are generally treated as two unrelated topics in the literature. The present article proposes a model to integrate fixed, random, and mixedeffects metaanalyses into the SEM framework. By applying an appropriate transformation on the data, studies in a metaanalysis can be analyzed as subjects in a structural equation model. This article also highlights some practical benefits of using the SEM approach to conduct a metaanalysis. Specifically, the SEMbased metaanalysis can be used to handle missing covariates, to quantify the heterogeneity of effect sizes, and to address the heterogeneity of effect sizes with mixture models. Examples are used to illustrate the equivalence between the conventional metaanalysis and the SEMbased metaanalysis. Future directions on and issues related to the SEMbased metaanalysis are discussed.
Exploring sources of reading comprehension difficulties among language minority learners and their classmates in early adolescence
 American Educational Research Journal
, 2010
"... This study explores the nature of reading comprehension difficulties among early adolescent language minority (LM) learners and native English speakers in urban schools. Sixthgrade students (399 LM learners, 182 native English speakers) were screened for difficulties, using a standardized measure ..."
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Cited by 9 (0 self)
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This study explores the nature of reading comprehension difficulties among early adolescent language minority (LM) learners and native English speakers in urban schools. Sixthgrade students (399 LM learners, 182 native English speakers) were screened for difficulties, using a standardized measure of reading comprehension. Of these, 262 students (201 LM learners, 61 native English speakers) with a score at or below the 35th percentile were administered measures of oral language and reading. More LM learners than their peers were classified as struggling readers (60 % vs. 40%, respectively). However, latent class analysis demonstrated that the two populations were evenly distributed among three skill profiles of struggling readers. Despite relative differences in word reading accuracy and fluency, each profile was characterized by low vocabulary knowledge. The majority of struggling readers were found to have developed basic fluency skills. The findings demonstrate the need for middle schools to identify why students are having comprehension difficulties and to target instruction to meet their specific needs, given the wide variation in the struggling reader population. Moreover, they suggest that treating LM learners as a separate group based on their status as secondlanguage learners may not be appropriate.
Detecting Social Desirability Bias Using Factor Mixture Models
, 2010
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Bayesian semiparametric structural equation models with latent variables
 Psychometrika
, 2010
"... Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions ..."
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Cited by 4 (2 self)
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Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identifiability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and efficient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.
Exploring the Latent Structures of Psychological Constructs in Social Development Using the
"... This paper provides an introduction to a recently developed conceptual framework— the dimensional–categorical spectrum—for utilizing general factor mixture models to explore the latent structures of psychological constructs. This framework offers advantages over traditional latent variable models th ..."
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This paper provides an introduction to a recently developed conceptual framework— the dimensional–categorical spectrum—for utilizing general factor mixture models to explore the latent structures of psychological constructs. This framework offers advantages over traditional latent variable models that usually employ either continuous latent factors or categorical latent class variables to characterize the latent structure and require an a priori assumption about the underlying nature of the construct as either purely dimension or purely categorical. The modeling process is discussed in detail and then illustrated with data on the delinquency items of Achenbach’s child behavior checklist from a sample of children in the National Adolescent and Child
Tests of measurement invariance without subgroups 1 Running head: TESTS OF MEASUREMENT INVARIANCE WITHOUT SUBGROUPS Tests of measurement invariance without subgroups: A generalization of classical methods
"... Tests of measurement invariance without subgroups 2 The issue of measurement invariance commonly arises in factoranalytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of gr ..."
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Cited by 3 (2 self)
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Tests of measurement invariance without subgroups 2 The issue of measurement invariance commonly arises in factoranalytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (1) identifying subgroups of individuals that violate measurement invariance along a continuous auxiliary variable without prespecified thresholds, and (2) identifying specific parameters impacted by measurement invariance violations. The tests are presented and illustrated in detail, including an application to a study of stereotype threat and simulations examining the tests ’ abilities in controlled conditions. Tests of measurement invariance without subgroups 3
A factor mixture analysis model for multivariate binary data
 Statistical Modelling
, 2012
"... ar ..."