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 likelihood-based 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 = 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test ...

Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study

For structural equation models, a huge variety of fit indices has been developed. These indices, however, can point to conflicting conclusions about the extent to which a model actually matches the observed data. The present article provides some guidelines that should help applied researchers to evaluate the adequacy of a given structural equation model. First, as goodness-of-fit measures depend on the method used for parameter estimation, maximum likelihood (ML) and weighted least squares (WLS) methods are introduced in the context of structural equation modeling. Then, the most common goodness-of-fit indices are discussed and some recommendations for practitioners given. Finally, we generated an artificial data set according to a "true" model and analyzed two misspecified and two correctly specified models as examples of poor model fit, adequate fit, and good fit.

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Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures.

Assessment in clinical psychology typically relies on global retrospective self-reports collected at research or clinic visits, which are limited by recall bias and are not well suited to address how behavior changes over time and across contexts. Ecological momentary assessment (EMA) involves repeated sampling of subjects’ current behaviors and experiences in real time, in subjects’ natural environments. EMA aims to minimize recall bias, maximize ecological validity, and allow study of microprocesses that influence behavior in real-world contexts. EMA studies assess particular events in subjects’ lives or assess subjects at periodic intervals, often by random time sampling, using technologies ranging from written diaries and telephones to electronic diaries and physiological sensors. We discuss the rationale for EMA, EMA designs, methodological and practical issues, and comparisons of EMA and recall data. EMA holds unique promise to advance the science and practice of clinical psychology by shedding ligh...

Ecological Momentary Assessment

Structural equation modeling (SEM) is a multivariate statistical framework that is used to model complex relationships between directly observed and indirectly observed (latent) variables. SEM is a general framework that involves simultaneously solving systems of linear equations and encompasses other techniques such as regression, factor analysis, path analysis, and latent growth curve modeling. Recently, SEM has gained popularity in the analysis of complex genetic traits because it can be used to better analyze the relationships between correlated variables (traits), to model genes as latent variables as a function of multiple observed genetic variants, and to assess the association between multiple genetic variants and multiple correlated phenotypes of interest. Though the general SEM framework only allows for the analysis of independent observations, recent work has extended SEM for the analysis of data on general pedigrees. Here, we review the theory of SEM for both unrelated and family data, describe the available software for SEM, and provide examples of SEM analysis.

Structural Equation Modeling

25. Multiple Imputation for Nonresponse in Surveys. By D. B. Rubin. ISBN 0 471 08705 X. Wiley, Chichester, 1987. 258 pp. £30.25.

Multiple Imputation for Nonresponse in Surveys

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 led to theories of multiple developmental pathways. Methods: This paper gives a brief overview of new methods that integrate variable- and person-centered analyses. Methods discussed include latent class analysis, latent transition analysis, latent class growth analysis, growth mixture modeling, and general growth mixture modeling. These methods are presented in a general latent variable modeling framework that expands traditional latent variable modeling by including not only continuous latent variables but also categorical latent variables. Results: Four examples that use the National Longitudinal Survey of Youth (NLSY) data are presented to illustrate latent class analysis, latent class growth analysis, growth mixture modeling, and general growth mixture modeling. Latent class analysis of antisocial behavior found four classes. Four heavy drinking trajectory classes were found. The relationship between the latent classes and background variables and consequences was studied. Conclusions: Person-centered and variable-centered analyses typically have been seen as different activities that use different types of models and software. This paper gives a brief overview of new methods that integrate variable- and person-centered analyses. The general framework makes it possible to combine these models and to study new models serving as a stimulus for asking research questions that have both person- and variable-centered aspects.

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Integrating Person-Centered and Variable-Centered Analyses: Growth Mixture Modeling With Latent Trajectory Classes

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 purpose of this article is to demonstrate how substantive researchers can use a Monte Carlo study to decide on sample size and determine power. Two models are used as examples, a confirmatory factor analysis (CFA) model and a growth model. The analyses are carried out using the Mplus program (Muthen& Muthen 1998).

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How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power

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 background characteristics changes over time. Method: The data used in this study are a general population sample (N = 7,859) from the National Longitudinal Survey of Youth (NLSY). This study uses a multivariate outcome approach that focuses on individual variation in trajectories over age. The statistical analysis uses random coefficients in a latent variable framework. Across-age changes in the importance of the influence of background variables on the outcomes are modeled using varying centering points. Results: A key finding is that dropping out of high school has no ...

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The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample

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Bayesian Analysis Using Mplus

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Linda K. Muthén

Papers

Integrating Person-Centered and Variable-Centered Analyses: Growth Mixture Modeling With Latent Trajectory Classes

How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power

The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample

Bayesian Analysis Using Mplus

Mplus Short Courses Topic 1 Exploratory Factor Analysis, Confirmatory Factor Analysis, And Structural Equation Modeling For Continuous Outcomes