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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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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.
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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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.
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 4 (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 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 3 (1 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,
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.
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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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.
Nonlinear Change Models in Populations with Unobserved Heterogeneity
"... Abstract. When unobserved heterogeneity exists in populations where the phenomenon of interest is governed by a functional form of change linear in its parameters, the growth mixture model (GMM) is useful for modeling change conditional on latent class. However, when the functional form of interest ..."
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Abstract. When unobserved heterogeneity exists in populations where the phenomenon of interest is governed by a functional form of change linear in its parameters, the growth mixture model (GMM) is useful for modeling change conditional on latent class. However, when the functional form of interest is nonlinear in its parameters, the GMM is not very useful because it is based on a system of equations linear in its parameters. The nonlinear change mixture model (NCMM) is proposed, which explicitly addresses unobserved heterogeneity in situations where change follows a nonlinear functional form. Due to the integration of nonlinear multilevel models and finite mixture models, neither of which generally have closed form solutions, analytic solutions do not generally exist for the NCMM. Five methods of parameter estimation are developed and evaluated with a comprehensive Monte Carlo simulation study. The simulation showed that the parameters of the NCMM can be accurately estimated with several of the proposed methods, and that the method of choice depends on the precise question of interest.
An Overview of Structural Equation Models and Recent Extensions
"... analysis is perhaps the first work that originated many of the key characteristics that still appear in contemporary SEMs. But the current SEMs have evolved, becoming more inclusive and general than even Wright probably ever imagined. SEMs represent a synthesis of knowledge about multivariate analys ..."
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analysis is perhaps the first work that originated many of the key characteristics that still appear in contemporary SEMs. But the current SEMs have evolved, becoming more inclusive and general than even Wright probably ever imagined. SEMs represent a synthesis of knowledge about multivariate analysis from econometrics, psychometrics, sociometrics (“quantitative sociology”), biostatistics, and statistics, though its development over the last 30 years has occurred mostly in the social and behavioral sciences. Indeed, it is only relatively recently that biostatistics and statistics have become interested in SEMs. Blalock (1964) and Duncan (1966) were early influential works that stimulated research in path analysis and SEM related procedures in sociology and the other social sciences. Two edited books that represent the early takeoff period of SEMs in the social sciences are Blalock (1971) and Goldberger and Duncan (1973). The LISREL software program (Jöreskog & Sörbom, 1978) was another major turning point that made sophisticated maximum
About the Authors
, 2002
"... The Faculty of Commerce Working Paper Series is intended to provide staff and students with a means of communicating new and evolving ideas in order to encourage academic debate. Working papers, as the title suggests, should not necessarily be taken as completed works or final expressions of opinion ..."
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The Faculty of Commerce Working Paper Series is intended to provide staff and students with a means of communicating new and evolving ideas in order to encourage academic debate. Working papers, as the title suggests, should not necessarily be taken as completed works or final expressions of opinions. All working papers are subject to review prior to publication by one or more editors or referees familiar with the discipline area. Normally, working papers may be freely quoted and/or reproduced provided proper reference to the author and source is given. When a working paper is published on a restricted basis,
POPULATIONS WHEN CLASS MEMBERSHIP IS UNKNOWN: DEFINING AND DEVELOPING THE LATENT CLASSIFICATION DIFFERENTIAL CHANGE MODEL
, 2005
"... by Kenneth Kelley III Standard methods for analyzing change generally assume that the population of interest is homogeneous or that heterogeneity is known. When a population consists of unknown subpopulations, the parameters within each of the latent classes may be unique to that particular class. I ..."
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by Kenneth Kelley III Standard methods for analyzing change generally assume that the population of interest is homogeneous or that heterogeneity is known. When a population consists of unknown subpopulations, the parameters within each of the latent classes may be unique to that particular class. In such a situation the results of standard techniques for analyzing change are misleading, because such methods ignore unobserved heterogeneity and treat the population as if it were homogeneous. The growth mixture model (GMM; Muthén, 2001a; Muthén, 2001b; Muthén, 2002) partly addresses the problem of unknown heterogeneity because the parameters of the GMM are conditional on latent class membership. However, the GMM is necessarily restricted to models of change linear in their parameters (such as polynomial change models). The latent classification