arXiv subjects

Peter M. Bentler

Publications and source records attributed to Peter M. Bentler.

3 recordsLinked to original sources

arXiv2024

Improved LM Test for Robust Model Specification Searches in Covariance Structure Analysis

Covariance Structure Analysis (CSA) or Structural Equation Modeling (SEM) is critical for political scientists measuring latent structural relationships, allowing for the simultaneous assessment of both latent and observed variables, alongside measurement error. Well-specified models are essential for theoretical support, balancing simplicity with optimal model fit. However, current approaches to improving model specification searches remain limited, making it challenging to capture all meaningful parameters and leaving models vulnerable to chance-based specification risks. To address this, we propose an improved Lagrange Multipliers (LM) test incorporating stepwise bootstrapping in LM and Wald tests to detect omitted parameters. Monte Carlo simulations and empirical applications underscore its effectiveness, particularly in small samples and models with high degrees of freedom, thereby enhancing statistical fit.

stat.ME↗

arXiv2024

Enhancing Model Fit Evaluation in SEM: Practical Tips for Optimizing Chi-Square Tests

This paper underscores the vital role of the chi-square test within political science research utilizing structural equation modeling (SEM). The ongoing debate regarding the inclusion of chi-square test statistics alongside fit indices in result presentations has sparked controversy. Despite the recognized limitations of relying solely on the chi-square test, its judicious application can enhance its effectiveness in evaluating model fit and specification. To exemplify this, we present three common scenarios pertinent to political science research where fit indices may inadequately address goodness-of-fit concerns, while the chi-square statistic can be effectively harnessed. Through Monte Carlo simulations, we examine strategies for enhancing chi-square tests within these scenarios, showcasing the potential of appropriately employed chi-square tests to provide a comprehensive model fit assessment. Our recommendation is to report both the chi-square test and fit indices, with a priority on precise model specification to ensure the trustworthiness of model fit indicators.

stat.AP↗

arXiv2021

Distributionally Weighted Least Squares in Structural Equation Modeling

In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal theory based methods such as maximum likelihood (ML) and normal theory based generalized least squares estimation (GLS) are unreliable. On the other hand, the asymptotically distribution free (ADF) estimator does not rely on any distribution assumption but cannot demonstrate its efficiency advantage with small and modest sample sizes. The methods which adopt misspecified loss functions including ridge GLS (RGLS) can provide better estimates and inferences than the normal theory based methods and the ADF estimator in some cases. We propose a distributionally-weighted least squares (DLS) estimator, and expect that it can perform better than the existing generalized least squares, because it combines normal theory based and ADF based generalized least squares estimation. Computer simulation results suggest that model-implied covariance based DLS (DLS_M) provided relatively accurate and efficient estimates in terms of RMSE. In addition, the empirical standard errors, the relative biases of standard error estimates, and the Type I error rates of the Jiang-Yuan rank adjusted model fit test statistic (T_JY) in DLS_M were competitive with the classical methods including ML, GLS, and RGLS. The performance of DLS_M depends on its tuning parameter a. We illustrate how to implement DLS_M and select the optimal a by a bootstrap procedure in a real data example.

stat.ME↗