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Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes
 Psychological Methods
, 2003
"... Growth mixture models are often used to determine if subgroups exist within the population that follow qualitatively distinct developmental trajectories. However, statistical theory developed for finite normal mixture models suggests that latent trajectory classes can be estimated even in the absenc ..."
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Cited by 89 (10 self)
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Growth mixture models are often used to determine if subgroups exist within the population that follow qualitatively distinct developmental trajectories. However, statistical theory developed for finite normal mixture models suggests that latent trajectory classes can be estimated even in the absence of population heterogeneity if the distribution of the repeated measures is nonnormal. By drawing on this theory, this article demonstrates that multiple trajectory classes can be estimated and appear optimal for nonnormal data even when only 1 group exists in the population. Further, the withinclass parameter estimates obtained from these models are largely uninterpretable. Significant predictive relationships may be obscured or spurious relationships identified. The implications of these results for applied research are highlighted, and future directions for quantitative developments are suggested. Over the last decade, random coefficient growth modeling has become a centerpiece of longitudinal data analysis. These models have been adopted enthusiastically by applied psychological researchers in part because they provide a more dynamic analysis of repeated measures data than do many traditional techniques. However, these methods are not ideally suited for testing theories that posit the existence of qualitatively different developmental pathways, that is, theories in which distinct developmental pathways are thought to hold within subpopulations. One widely cited theory of this type is Moffitt’s (1993) distinction between “lifecourse persistent ” and “adolescentlimited ” antisocial behavior trajectories. Moffitt’s theory is prototypical of other developmental taxonomies that have been proposed in such diverse areas as developmental psychopathology (Schulenberg,
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
Bayesian Estimation and Testing of Structural Equation Models
 Psychometrika
, 1999
"... The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameter ..."
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Cited by 45 (10 self)
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The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errorsinvariables model.
Testing main effects and interactions in latent curve analysis
 Psychological Methods
, 2004
"... A key strength of latent curve analysis (LCA) is the ability to model individual variability in rates of change as a function of 1 or more explanatory variables. The measurement of time plays a critical role because the explanatory variables multiplicatively interact with time in the prediction of t ..."
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Cited by 14 (4 self)
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A key strength of latent curve analysis (LCA) is the ability to model individual variability in rates of change as a function of 1 or more explanatory variables. The measurement of time plays a critical role because the explanatory variables multiplicatively interact with time in the prediction of the repeated measures. However, this interaction is not typically capitalized on in LCA because the measure of time is rather subtly incorporated via the factor loading matrix. The authors ’ goal is to demonstrate both analytically and empirically that classic techniques for probing interactions in multiple regression can be generalized to LCA. A worked example is presented, and the use of these techniques is recommended whenever estimating conditional LCAs in practice. Randomeffects growth models have become increasingly popular in applied behavioral and social science research. The two primary approaches used for estimating these models are the hierarchical linear model (HLM; Bryk & Raudenbush, 1987; Raudenbush & Bryk, 2002) and structural equationbased latent curve analysis (LCA; Meredith & Tisak, 1984, 1990).1 The variable measuring the passage of time plays a critical role in both the HLM and LCA approaches, although the way in which this measure is incorporated into the model is quite different. The HLM approach explicitly incorporates the measure of time as an exogenous predictor variable within the Level 1, or personlevel, equation. In contrast, the LCA approach incorporates the measure of time by placing specific restrictions on the values of the factor loading matrix that relate the repeated measures to the underlying latent growth factors. In many situations these two approaches to growth modeling are analytically equivalent, whereas in other situations they are not (e.g., MacCallum, Kim, Malarkey, & KiecoltGlaser,
Quasi Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects
"... The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficie ..."
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Cited by 14 (0 self)
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The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficient methods is complicated by the fact that a nonlinear model structure implies specifically nonnormal multivariate distributions for the indicator variables. In this paper, nonlinear structural equation models with quadratic forms are introduced and a new QuasiMaximum Likelihood method for simultaneous estimation of model parameters is developed with the focus on statistical efficiency and computational practicability. The QuasiML method is based on an approximation of the nonnormal density function of the joint indicator vector by a product of a normal and a conditionally normal density. The results of MonteCarlo studies for the new QuasiML method indicate that the parameter estimation is almost as efficient as ML estimation, whereas ML estimation is only computationally practical for elementary models. Also, the QuasiML method outperforms other currently available methods with respect to efficiency. It is demonstrated in a MonteCarlo study that the QuasiML method permits computationally feasible and very efficient analysis of models with multiple latent nonlinear effects. Finally, the applicability of the QuasiML method is illustrated by an empirical example of an aging study in psychology. Key words: structural equation modeling, quadratic form of normal variates, latent interaction effect, moderator effect, QuasiML estimation, variance function model. 1 1.
ENCOURAGING BEST PRACTICE IN QUANTITATIVE MANAGEMENT RESEARCH: AN INCOMPLETE LIST OF OPPORTUNITIES
"... The paper identifies some common problems encountered in quantitative methodology and provides information on current best practice to resolve these problems. We first discuss issues pertaining to variable measurement and concerns regarding the underlying relationships among variables. We then highl ..."
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Cited by 11 (0 self)
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The paper identifies some common problems encountered in quantitative methodology and provides information on current best practice to resolve these problems. We first discuss issues pertaining to variable measurement and concerns regarding the underlying relationships among variables. We then highlight several advances in estimation methodology that may circumvent issues encountered in common practice. Finally, we discuss approaches that move beyond existing research designs, including the development and use of datasets that embody linkages across levels of analysis, or combine qualitative and quantitative methods.
Testing Negative Error Variances: Is a Heywood Case a Symptom of Misspecification
 Sociological Methods & Research
, 2012
"... Negative sample estimates of the variances of disturbances or errors are a common occurrence in factor analysis and structural equation models. Given the impossibility of these values in the population, researchers need to determine the reason for their occurrence. Otherwise the results of the rest ..."
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Negative sample estimates of the variances of disturbances or errors are a common occurrence in factor analysis and structural equation models. Given the impossibility of these values in the population, researchers need to determine the reason for their occurrence. Otherwise the results of the rest of the analysis are likely to be deemed untrustworthy. There is not a single cause of negative error variances or ”Heywood cases.”
Partial Least Squares: A critical review and a potential alternative
 Proceedings of the Administrative Sciences Association of Canada (ASAC ) Conference
, 2005
"... This paper provides a critique of the perceived advantages of PLS over covariancebased methods for estimating structural equation (SEM) models. Specific attention is drawn to the lack of consistency of PLS estimates. The two stage least squares method of estimation is described, proposed as a potent ..."
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Cited by 6 (0 self)
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This paper provides a critique of the perceived advantages of PLS over covariancebased methods for estimating structural equation (SEM) models. Specific attention is drawn to the lack of consistency of PLS estimates. The two stage least squares method of estimation is described, proposed as a potential alternative, and compared with PLS in a simulation study.
Modeling Interactions Between Latent and Observed Continuous Variables Using MaximumLikelihood Estimation In Mplus
, 2003
"... Modeling with random slopes is used in random coefficient regression, multilevel regression, and growth modeling. Random slopes can be seen as continuous latent variables. Recently, a flexible modeling framework has been implemented in the Mplus program to do modeling with such latent variables comb ..."
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Modeling with random slopes is used in random coefficient regression, multilevel regression, and growth modeling. Random slopes can be seen as continuous latent variables. Recently, a flexible modeling framework has been implemented in the Mplus program to do modeling with such latent variables combined with modeling of psychometric constructs, typically referred to as factors, measured by multiple indicators. This note shows how such a framework can handle interactions between latent continuous and observed continuous indicators. Three examples are given: a Monte Carlo simulation to estimate power to detect the interaction; a psychological example; and a growth modeling example. Mplus input, output, and data are available at the Mplus web site, www.statmodel.com/mplus/examples/webnote.html. 1 1
TwoStage Least Squares (2SLS) and Structural Equation Models (SEM). http://csusap.csu. edu.au./~eoczkows/home.htm Samuel Gebreselassie and E. Ludi (2007), Agricultural Commercialisation in Coffeegrowing Areas of Ethiopia. Paper presented at the
 Fifth International Conference on the Ethiopian
, 2003
"... These notes describe the 2SLS estimator for latent variable models developed by Bollen (1996). The technique separately estimates the measurement model and structural model of SEM. One can therefore use it either as a stand alone procedure for a full SEM or combine it with factor analysis, for examp ..."
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These notes describe the 2SLS estimator for latent variable models developed by Bollen (1996). The technique separately estimates the measurement model and structural model of SEM. One can therefore use it either as a stand alone procedure for a full SEM or combine it with factor analysis, for example, establish the measurement model using factor analysis and then employ 2SLS for the structural model only. The advantages of using 2SLS over the more conventional maximum likelihood (ML) method for SEM include: • It does not require any distributional assumptions for RHS independent variables, they can be nonnormal, binary, etc. • In the context of a multiequation nonrecursive SEM it isolates specification errors to single equations, see Bollen (2001). • It is computationally simple and does not require the use of numerical optimisation algorithms. • It easily caters for nonlinear and interactions effects, see Bollen and Paxton (1998). • It permits the routine use of often ignored diagnostic testing procedures for problems such as heteroscedasticity and specification error, see Pesaran and Taylor (1999). • Simulation evidence from econometrics suggests that 2SLS may perform better in small samples than ML, see Bollen (1996, pp120121). There are however some disadvantages in using 2SLS compared to ML, these include: • The ML estimator is more efficient than 2SLS given its simultaneous estimation of all relationships, hence ML will dominate 2SLS always in sufficiently large samples if all assumptions are valid and the model specification is correct. Effectively ML is more efficient (if the model is valid) as it uses much more information than 2SLS. • Unlike the ML method, the 2SLS estimator depends upon the choice of reference variable. The implication being that different 2SLS estimates result given different scaling variables. • Programs with diagram facilities such as EQS do not exist for 2SLS. One needs to logically work through the structure of the model to specify individual equations for all the relationships for the 2SLS estimator.