A partially confirmatory approach to scale development with the Bayesian Lasso.

Abstract

The exploratory and confirmatory approaches of factor analysis lie on two ends of a continuum of substantive input for scale development. Recent advancements in Bayesian regularization methods enable more flexibility in covering a wide range of the substantive continuum. Based on the Bayesian Lasso (least absolute shrinkage and selection operator) methods for the regression model and covariance matrix, this research proposes a partially confirmatory approach to address the loading and residual structures at the same time. With at least one specified loading per item, a one-step procedure can be applied to figure out both structures simultaneously. With a few specified loadings per factor, a two-step procedure is preferred to capture the model configuration correctly. In both cases, the Bayesian hierarchical formulation is implemented using Markov Chain Monte Carlo estimation with different Lasso or regular priors. Both simulated and real data sets were analyzed to evaluate the validity, robustness, and practical usefulness of the proposed approach across different situations.

Bayesian regularization in multiple-indicators multiple-causes models.

“…To achieve a better balance between parameter selection and estimation, research on alternative priors has been developed. J. Chen et al (2021) proposed a one-step analysis using Bayesian lasso and found that lasso outperformed ridge in reducing the bias of estimates and controlling false positive rates in CFA.…”

“…Muthén & Muthén, 1998–2017). Other penalty priors are more challenging to implement but have been demonstrated in a few studies to offer an improved balance between variable selection and model estimation (e.g., Brown & Griffin, 2010; J. Chen et al, 2021; Lu et al, 2016).…”

“…Research in Bayesian regularization has mostly focused on the measurement components of SEM. Specifically, penalty priors such as ridge, lasso, and SSP have been extended to confirmatory factor analysis (CFA) for detecting cross-loadings and residual correlations (J. Chen et al, 2021; Lu et al, 2016; B.…”

“…If sparsity is desired, lasso is commonly chosen over the ridge. Bayesian lasso has been applied to CFA to identify cross-loadings and residual correlations (J. Chen et al, 2021) and also adopted in empirical analyses to allow the residuals to correlate in CFA (e.g., Overmeyer et al, 2020).…”

“…The hyperparameters of penalty priors were set at preassigned values for ridge: normalσ2=0.01 (B. Muthén & Asparouhov, 2012), for lasso and alasso: normalαl=1,normalβl=0.01 (J. Chen et al, 2021), for SSP: normalσnormalp2=0.001,cnormalp2∼IGfalse(0.5,0.5false) (Van Erp et al, 2019), and for horseshoe: normalρnormalp∼C+false(0,1false),υ∼C+false(0,1false) (Polson & Sokolov, 2019).…”