Criteria for Parameter Identification in Bayesian Lasso Methods for Covariance Analysis: Comparing Rules for Thresholding, p-value, and Credible Interval

ABSTRACT

The lasso is a commonly used regularization method that is increasing used in structural equation models (SEMs). Under the Bayesian framework, lasso is rendered more flexible and readily produces estimates of standard errors and the penalty parameter. However, in practice, it remains unclear what decision rule is appropriate for parameter identification; in other words, determining what size estimate is large enough to be included into the model. The current study compared three decision rules for parameter identification – thresholding, p-value, and credible interval in confirmatory factor analysis. Specifically, two distinct parameter spaces were studied: cross-loadings and residual correlations. Results showed that the thresholding rule performed best in balancing power and Type I error rate. Different thresholds for standardized estimates were needed for different conditions. Guidelines for parameter identification and recommended thresholding values were also provided. Results of the current study have the potential to extend to a broad range of SEMs.

KEYWORDS:

• Confirmatory factor analysis
• cross-loading
• residual correlation
• regularization

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ We also checked the performance of the z-test, and results were similar to but slightly worse than the 95% HPD interval. Results based on the z-test are not reported in the current paper. Note that the worse performance of z-test may be due to the non-normal property of Lasso regularized parameters (Pötscher & Leeb, 2009).

Additional information

Funding

This work was funded by the National Natural Science Foundation of China under Grant [31871128]; the MOE (Ministry of Education) Project of Humanities and Social Science of China under Grant [18YJA190013], the NSF Grant (SES-1424875) and an NIH Grant (1UL1TR001420-01) from the United States.