Results 1  10
of
14
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 ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
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.
Moderated multiple regression, spurious interaction effects
 and IRT. Applied Psychological Measurement
, 2005
"... explore the Type I error rates in moderated multiple regression (MMR) of observed scores and estimated latent trait scores from a twoparameter logistic item response theory (IRT) model. The results of both studies showed that MMR Type I error rates were substantially higher than the nominal alpha ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
explore the Type I error rates in moderated multiple regression (MMR) of observed scores and estimated latent trait scores from a twoparameter logistic item response theory (IRT) model. The results of both studies showed that MMR Type I error rates were substantially higher than the nominal alpha levels when scale scores were composed of summed binary item responses (e.g., true/false, yes/no, disagree/agree items). Performing the regression analyses on estimated trait scores (θ ̂ ) from a twoparameter logistic model improved the error detection rates considerably. That is, the Type I error rates for spurious interaction effects were similar to the nominal alpha levels under most conditions. These findings
Maximum likelihood and Bayesian estimation for nonlinear structural equation models
, 2007
"... Structural equation modeling (SEM) began at its roots as a method for modeling linear relationships among latent variables. The wellknown software for SEM name LISREL (Jöreskog and Sörbom, 1996) stands for “Linear Structural Relations”. But, in many cases, the restriction to linearity is not ad ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Structural equation modeling (SEM) began at its roots as a method for modeling linear relationships among latent variables. The wellknown software for SEM name LISREL (Jöreskog and Sörbom, 1996) stands for “Linear Structural Relations”. But, in many cases, the restriction to linearity is not adequate or flexible enough to explain the phenomena of interest.
Psychology
, 2013
"... This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations 19112013 by an authorized administrator of ScholarWorks@UMass Amherst. For more ..."
Abstract
 Add to MetaCart
This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations 19112013 by an authorized administrator of ScholarWorks@UMass Amherst. For more
Assessing Spurious Interaction Effects in Structural Equation
"... epm.sagepub.com ..."
(Show Context)
Isotone additive latent variable models
, 2011
"... additive latent variable models ..."
(Show Context)
A Bayesian Approach for Multigroup Nonlinear Factor Analysis
"... The main purpose of this article is to develop a Bayesian approach for a general multigroup nonlinear factor analysis model. Joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups are obtained simultaneously. A hybrid algori ..."
Abstract
 Add to MetaCart
(Show Context)
The main purpose of this article is to develop a Bayesian approach for a general multigroup nonlinear factor analysis model. Joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups are obtained simultaneously. A hybrid algorithm that combines the MetropolisHastings algorithm and the Gibbs sampler is implemented to produce these joint Bayesian estimates. It is shown that this algorithm is computationally efficient. The Bayes factor approach is introduced for comparing models under various degrees of invariance across groups. The Schwarz criterion (BIC), a simple and useful approximation of the Bayes factor, is calculated on the basis of simulated observations from the Gibbs sampler. Efficiency and flexibility of the proposed Bayesian procedure are illustrated by some simulation results and a reallife example. Factor analysis is an important technique in behavioral science research for assessing interdependence and correlations among observed variables and latent factors. In a linear factor analysis model, a set of manifest variables is expressed as a linear combination of a relatively small number of latent variables, called factors, and a residual vector. There is a strong demand to extend linear models to nonlinear models since nonlinear relationships such as the quadratic and interaction terms of the latent factors are found to be important in establishing substantive theories in many fields. For example, see
Comparing TwoStage Approaches to Detect Continuous Manifest Moderating Effects on Construct Relationships
, 2008
"... In this study, seven twostage approaches in detecting continuous manifest moderating effects on construct relationships are compared in terms of bias and power by using Monte Carlo simulation. The simulation is conducted for each of the conditions formed by different skewness, kurtosis and intercor ..."
Abstract
 Add to MetaCart
In this study, seven twostage approaches in detecting continuous manifest moderating effects on construct relationships are compared in terms of bias and power by using Monte Carlo simulation. The simulation is conducted for each of the conditions formed by different skewness, kurtosis and intercorrelations for exogenous constructs and the moderator, different factor loadings, error variances, and sample sizes under specified models. The results indicate that different approaches tend to produce little bias difference but lead to power difference, varying with different situations. Recommendations for the proper use of the twostage approaches are provided based on the simulation results obtained.
Is There Any Interaction Effect Between Intention and Perceived Behavioral Control?
"... Many models in social psychology, which have been developed to explain behavior, postulate interaction effects between explanatory latent variables. In the last years, there have been many new developments for estimating interactions between latent variables in structural equation modeling. However, ..."
Abstract
 Add to MetaCart
(Show Context)
Many models in social psychology, which have been developed to explain behavior, postulate interaction effects between explanatory latent variables. In the last years, there have been many new developments for estimating interactions between latent variables in structural equation modeling. However, there have been very few applications with real data from theorydriven studies. This paper provides an empirical test with real data from an ongoing research project about travel mode choice in Frankfurt, using the theory of planned behavior. We apply three statistical approaches for the estimation of interaction effects between the latent variables perceived behavioral control (PBC) and intention for predicting travel mode choice (behavior): latent variable scores, maximum likelihood and robust maximum likelihood. We compare the strengths and weaknesses of the approaches from an applied point of view. In a metaanalytic review we summarize the results of 14 articles, which estimated the interaction between intention and PBC for predicting behavior, and discuss the problems associated with such a metaanalysis.
Title of Document: A COMPARISON OF METHODS FOR TESTING FOR INTERACTION EFFECTS IN STRUCTURAL EQUATION MODELING
"... The current study aimed to determine the best method for estimating latent variable interactions as a function of the size of the interaction effect, sample size, the loadings of the indicators, the size of the relation between the firstorder latent variables, and normality. Data were simulated fro ..."
Abstract
 Add to MetaCart
The current study aimed to determine the best method for estimating latent variable interactions as a function of the size of the interaction effect, sample size, the loadings of the indicators, the size of the relation between the firstorder latent variables, and normality. Data were simulated from known population parameters, and data were analyzed using nine latent variable methods of testing for interaction effects. Evaluation criteria used for comparing the methods included proportion of relative bias, the standard deviation of parameter estimates, the mean standard error estimate, a relative ratio of the mean standard error estimate to the standard deviation of parameter estimates, the percent of converged solutions, Type I error rates, and empirical power. It was found that when data were normally distributed and the sample size was 250 or more, the constrained approach results in the least biased estimates of the interaction effect, had the most accurate standard error estimates, high convergence rates, and adequate type I error rates and power. However, when sample sizes were small and the loadings were of adequate size, the latent variable scores approach may be preferable to the constrained approach. When data were severely nonnormal, all of the methods were biased, had inaccurate