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Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data
, 2004
"... 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. ..."
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Cited by 160 (16 self)
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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
 Psychological Methods
, 2005
"... 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 ..."
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Cited by 73 (4 self)
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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 population heterogeneity. Observed sources of heterogeneity can be included as covariates. The different ways to incorporate covariates correspond to different conceptual interpretations. These are discussed in detail. Characteristics of factor mixture modeling are described in comparison to other methods designed for data stemming from heterogeneous populations. A stepbystep analysis of a subset of data from the Longitudinal Survey of American Youth illustrates how factor mixture models can be applied in an exploratory fashion to data collected at a single time point. The populations investigated in the behavioral sciences and related fields of research are often heterogeneous. A sample may consist of explicitly defined groups such as experimental and control groups, and the aim is to compare these groups. On the other hand, the sources of population heterogeneity may not be known beforehand. Test scores on a cognitive test may reflect two types of children in the sample: those who master the knowledge required to solve the items (masters) and those who lack this critical knowledge (nonmasters). The interest may be to decide to which of the subpopulations a given child most likely belongs. In addition, it may be of interest to characterize masters and nonmasters using background variables to develop specific
The integration of continuous and discrete latent variable models: Potential problems and promising opportunities
 Psychological Methods
, 2004
"... Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes i ..."
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Cited by 48 (6 self)
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Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model, nonnormal continuous measures, and nonlinear relationships among observed and/or latent variables. When the objective of a SEMM analysis is the identification of latent classes, these conditions should be considered as alternative hypotheses and results should be interpreted cautiously. However, armed with greater knowledge about the estimation of SEMMs in practice, researchers can exploit the flexibility of the model to gain a fuller understanding of the phenomenon under study. In recent years, many exciting developments have taken place in structural equation modeling, but perhaps none more so than the development of structural equation models that account for unobserved popula
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 28 (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,
Trajectories of Alcohol and Drug Use and Dependence from Adolescence to Adulthood: The Effects of Familial Alcoholism and Personality
 Journal of Abnormal Psychology
, 2004
"... This study describes trajectories of substance use and dependence from adolescence to adulthood. Identified consumption groups include heavy drinking/heavy drug use, moderate drinking/experimental drug use, and light drinking/rare drug use. Dependence groups include alcohol only, drug only, and como ..."
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Cited by 28 (4 self)
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This study describes trajectories of substance use and dependence from adolescence to adulthood. Identified consumption groups include heavy drinking/heavy drug use, moderate drinking/experimental drug use, and light drinking/rare drug use. Dependence groups include alcohol only, drug only, and comorbid groups. The heavy drinking/heavy drug use group was at risk for alcohol and drug dependence and persistent dependence and showed more familial alcoholism, negative emotionality, and low constraint. The moderate drinking/experimental drug use group was at risk for alcohol dependence but not comorbid or persistent dependence and showed less negative emotionality and higher constraint. Familial alcoholism raised risk for alcohol and drug use and dependence in part because children from alcoholic families were more impulsive and lower in agreeableness. Substance use and substance use disorders show systematic agerelated patterns, with adolescent onset, peaks in use and diagnosed disorders in “emerging adulthood ” (ages 18–25; Arnett, 2000), and declines in use after the midtwenties (Bachman, Wadsworth, O’Malley, Johnston, & Schulenberg, 1997; Chen & Kandel, 1995). However, despite these overall trends, there is also consid
Classroom effects on children’s achievement trajectories in elementary school
 In
, 2008
"... This nonexperimental, longitudinal field study examines the extent to which variation in observed classroom supports (quality of emotional and instructional interactions and amount of exposure to literacy and math activities) predicts trajectories of achievement in reading and math from 54 months t ..."
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Cited by 27 (1 self)
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This nonexperimental, longitudinal field study examines the extent to which variation in observed classroom supports (quality of emotional and instructional interactions and amount of exposure to literacy and math activities) predicts trajectories of achievement in reading and math from 54 months to fifth grade. Growth mixture modeling detected two latent classes of readers: fast readers whose skills developed rapidly and leveled off, and a typical group for which reading growth was somewhat less rapid. Only one latent class was identified for math achievement. For reading, there were small positive associations between observed emotional quality of teacherchild interactions and growth. Growth in math achievement showed small positive relations with observed emotional interactions and exposure to math activities. There was a significant interaction between quality and quantity of instruction for reading such that at higher levels of emotional quality there was less of a negative association between amount of literacy exposure and reading growth.
The use of latent trajectory models in psychopathology research
 Journal of Abnormal Psychology
, 2003
"... Despite the recent surge in the development of powerful modeling strategies to test questions about individual differences in stability and change over time, these methods are not currently widely used in psychopathology research. In an attempt to further the dissemination of these new methods, the ..."
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Cited by 23 (1 self)
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Despite the recent surge in the development of powerful modeling strategies to test questions about individual differences in stability and change over time, these methods are not currently widely used in psychopathology research. In an attempt to further the dissemination of these new methods, the authors present a pedagogical introduction to the structural equation modeling based latent trajectory model, or LTM. They review several different types of LTMs, discuss matching an optimal LTM to a given question of interest, and highlight several issues that might be particularly salient for research in psychopathology. The authors augment each section with a review of published applications of these methods in psychopathologyrelated research to demonstrate the implementation and interpretation of LTMs in practice. As described in the masthead, the Journal of Abnormal Psychology is dedicated to the publication of articles that explore the correlates and determinants of abnormal behavior. Among other aspects of study, it is stated that “Each article should represent an addition to knowledge and understanding of abnormal behavior in its etiology, description, or change. ” One powerful method that can
Overextraction of latent trajectory classes: Much ado about nothing? Reply to Rindskopf
 2003), Muthén (2003), and Cudeck and Henly (2003). Psychological Methods
"... 1st theme is that modelchecking procedures may be capable of distinguishing between mixtures of normal and homogeneous nonnormal distributions. Although useful for assessing model quality, it is argued here that currently available procedures may not always help discern between these 2 possibiliti ..."
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Cited by 23 (4 self)
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1st theme is that modelchecking procedures may be capable of distinguishing between mixtures of normal and homogeneous nonnormal distributions. Although useful for assessing model quality, it is argued here that currently available procedures may not always help discern between these 2 possibilities. The 2nd theme is that even if these 2 possibilities cannot be distinguished, a growth mixture model may still provide useful insights into the data. It is argued here that whereas this may be true for the scientific goals of description and prediction, the acceptance of a model that fundamentally misrepresents the underlying data structure may be less useful in pursuit of the goal of explanation. We begin by thanking Robert Cudeck, Susan Henly, Bengt Muthén, and David Rindskopf for providing comments on our work (Bauer & Curran, 2003). We could not have asked for a more talented and esteemed group of quantitative methodologists to comment on our article, and we greatly appreciate the
Local solutions in the estimation of growth mixture models
 PsychologicalMethods
, 2006
"... Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified ..."
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Cited by 21 (3 self)
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Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however, local solutions may still be problematic. Results from an empirical case study and a small Monte Carlo simulation show that failure to thoroughly consider the possible presence of local optima in the estimation of a growth mixture model can sometimes have serious consequences, possibly leading to adoption of an inferior solution that differs in substantively important ways from the actual maximum likelihood solution. Often, the defaults of current software need to be overridden to thoroughly evaluate the parameter space and obtain confidence that the maximum likelihood solution has in fact been obtained.