# Your search: "author:Bentler, Peter M"

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## Scholarly Works (33 results)

Although coefficient alpha is the most widely used measure of internal consistency, it does not optimally describe the unidimensional internal consistency of a composite. Coefficients based on a one-factor model have been suggested as improved estimators of internal consistency reliability. When the 1-factor model does not fit the data, however, the meaning of such a coefficient is unclear. A new identification condition for factor analytic models is proposed that assures the composite can be modeled with only one common factor. The associated 1-factor reliability is the maximal internal consistency coefficient for a unit-weighted composite. The coefficient also describes k-factor reliability, the greatest lower bound to reliability, and reliability for any composite from a latent variable model with additive errors.

In the traditional model comparison procedure, two nested structural models are hypothesized to be equal under some constraints, e.g., equality constraints. A strict null hypothesis is then evaluated by statistical tests to decide on the acceptance or rejection of the restrictions that differentiate the models. We propose instead to evaluate model close match, using the distance between two models in terms of the Kullback-Leibler (1951) Information Criterion, either as important supplementary information or as a criterion for nested structured model comparison. Based on the results of Vuong (1989) and Yuan, Hayashi and Bentler (2005), we develop some ADF-like generalized RMSEA tests for inference on model closeness. Simulation studies show that our proposed tests have robust and desirable performance in spite of severe nonnormality across several examples when sample size is as large as 150, and its relevance to educational research is shown with models for some TOEFL data. Consequently, a two-stage procedure which combines the traditional nested model comparison and the additional inferential information regarding model close match is further suggested to improve the typical practice of structured model modification.

Problems about whether a hypothesized covariance structure models is an appropriate representation of the population covariance structure of multiple variables can be addressed using goodness-of-fit testing in structural equation modeling. Many test statistics and their extensions have been developed for various specific conditions and some of them have been extensively used in practice. However, their expected performances might break down under violations of multivariate normality or sufficiently large sample sizes. This paper evaluates the robustness of four modified goodness-of-fit test statistics T_{SB(new)}, T_{MV}, T_{YB} and T_{F} in SEM. Monte Carlo simulation demonstrates that the robustness of covariance structure statistics vary as a function of the correctness of the model as well as distributional characteristics of observed data. Suggestions for application of these modified test statistics are given after taking both the literature and current simulation result into account. A surprising result was the failure of T_{MV}, the Satorra-Bentler mean-scaled and variance-adjusted test statistic, to perform correctly even asymptotically in one condition.

One of the main problems of statistical inference in Structural Equation Modeling (SEM) is the overall goodness of fit test. Many statistical theories have been developed based on asymptotic distributions of test statistics. When the model includes a large number of variables or the population is not from the multivariate normal distribution, the rates of convergence of these asymptotic distributions are very slow, and thus in these situations the asymptotic distributions do not approximate the distribution of the test statistics very well. Modifications to theoretical models and also bootstrap methods have been developed by researchers to improve the accuracy of hypothesis testing, mainly accuracy of Type I error, but when the sample size is small or the number of variables is large those methods have their limitations. Here we propose a Monte Carlo test that is able to control Type I error with more accuracy and it overcomes some of the limitations in the bootstrapping and theoretical approaches. Our simulation study shows that the suggested Monte Carlo test has more accurate observed significance level, as compared to other tests. Problems that occur in the bootstrapping are highlighted and it is shown that the new Monte Carlo test can overcome those problems. A power analysis shows that the new test has a reasonable power.

The factor analytic model is usually an approximation that may not represent well the latent structure of a set of variables. This paper studies the distortion to common factor analysis due to doublets, pairwise associations in variables over and above those postulated by the factor model. Three methodologies to estimate the parameters of the factor model while minimizing the influence of doublets on the solution, i.e., methodologies that are resistant to the effects of doublets and near doublets, proposed by Yates(1987), Mulaik(2010) and Bentler(2012), are reviewed and compared. Examples and a simulation verify that these methodologies achieve their goal.