Maximum likelihood estimation of nonlinear structural equation models

Lee, Sik Yum; Zhu, Hong

doi:10.1007/bf02294842

Cited by 98 publications

(74 citation statements)

References 46 publications

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“…Defining the joint density of the latent and the observed variables is not very difficult; however, integrating out the latent variables to get the proper likelihood function results in a rather unattractive multivariate integral. There are several ways to tackle this problem, see Klein and Moosbrugger (2000), Lee and Zhu (2002), and Klein (2007), to mention just a few publications. The SEM software Mplus of Muthén (1998-2007) has also an option to deal with these kinds of interaction models under the normality assumption for the regressors.…”

Section: Discussionmentioning

confidence: 99%

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

Mooijaart

Satorra

2009

Psychometrika

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In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may, in fact, be severely nonlinear. In addition, the present paper shows that such insensitivity to nonlinear terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.

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Section: Discussionmentioning

confidence: 99%

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

Mooijaart

Satorra

2009

Psychometrika

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“…Several studies have been completed which rely on fewer replications and an ANOVA approach to analysis (e.g., 100 replications as reported in Kankaraš, Vermunt, & Moors, 2011;Lee, Song, & Lee, 2003;Lee & Xia, 2008;Lee & Zhu, 2002; Song, Lee, & Hser, 2008;and 200 replications as reported in Fan, Thompson, & Wang, 1999;Hu & Bentler, 1999;Jackson, 2003Jackson, , 2007. The plsSEM package (Monecke & Leisch, 2012) developed for R (R Development Core Team, 2012) was used to obtain model parameter and standard error estimates.…”

Section: Simulation Designmentioning

confidence: 99%

Evaluation of partial least squares parameter recovery

Chumney

2015

Proceedings of the 2nd International Symposium on Partial Least Squares Path Modeling: The Conference for PLS Users

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The purpose of this study was to evaluate the performance of Partial Least Squares under lessthan-ideal conditions selected to imitate real-world data. A simulation study with a 3×3×2×2 design was conducted. The design and data features of interest were sample size (50, 300, 1000), number of items per latent variable (3, 5, 7), degree of model misspecification (correctly specified, misspecified), and nature of the relationships between items and latent variables in the measurement models (reflective, formative). Bias of model parameter estimates, and bias and accuracy of standard error estimates were examined to evaluate the performance of PLS for each experimental condition.

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“…developed a Bayesian approach for estimation and model comparison. For maximum likelihood (ML) estimation, Lee and Zhu (2002) developed a procedure via a Monte Carlo EM algorithm (Dempster, Laird & Rubin, 1977;Wei & Tanner, 1990). Results from a comparative study (Lee, Song, &Poon, 2004) indicate that the Bayesian and ML approaches are in general better than the product indicator approaches.…”

Section: Introductionmentioning

confidence: 98%

“…We will apply the MCECM algorithm (Lee & Zhu, 2002) for ML estimation of the model; then in the local influence analysis we will focus on a displacement function that depends on the conditional expectation obtained at the E-step of the MCECM algorithm rather than the more complicated observed-data likelihood displacement as in Cook's (1986) approach. The well-known Metropolis-Hastings (MH) algorithm (Hastings, 1970;Metropolis, Rosenbluth, Rosenbluth, Teller, & Teller, 1953) will be used to generate a sufficiently large number of observations from the appropriate conditional distributions for creating the building blocks in the diagnostic measures.…”

Section: Introductionmentioning

confidence: 99%