An Adaptive Bayesian Lasso Approach with Spike-and-Slab Priors to Identify Multiple Linear and Nonlinear Effects in Structural Equation Models

In applied research, such as with motivation theories, typically many variables are theoretically implied predictors of an outcome and several interactions are assumed (e.g., Watt, 2004). However, estimation problems that might arise when several interaction and/or quadratic effects are analyzed simultaneously have not been investigated because simulation studies on interaction effects in the structural equation modeling framework have mainly focused on small models that contain single interaction effects. In this article, we show that traditional approaches can provide estimates with low accuracy when complex models are estimated. We introduce an adaptive Bayesian lasso approach with spike-and-slab priors that overcomes this problem. Using a complex model in a simulation study, we show that the parameter estimates of the proposed approach are more accurate in situations with high multicollinearity or low reliability compared with a standard Bayesian lasso approach and typical frequentist approaches (i.e., unconstrained product indicator approach and latent moderated structures approach).