Criteria for Parameter Identification in Bayesian Lasso Methods for Covariance Analysis: Comparing Rules for Thresholding, p-value, and Credible Interval. Issue 6 (2nd November 2021) - Zhang, Lijin; Pan, Junhao; Ip, Edward Haksing
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.