Bayesian Nonlinear Modeling with Many Predictors

By using smooth effect for predictors, a researcher is relieved of the burden of assuming a specific functional form for how a predictor influences the response variable. For a data set with many predictors, estimation of smooth effects might become difficult computationally, and overfitting might occur. Our research overcomes these issues by using the Spike and Slab Generalized Additive Model (SSGAM) proposed by Scheipl et al. (2012). This Bayesian method estimates smooth effects, including interaction effects, and shrinks small effects to prevent overfitting. The contribution of our paper is to make this methodology feasible for a data set with many predictors. We propose to apply a first step of variable selection with DART proposed by Linero (2018), which performs variable selection with a Bayesian modification of a decision tree ensemble. In this way, we can estimate smooth effects for a data sets with many predictors. Our proposed methodology is used to model the choice of viewing a premiere of a new TV series on prime time TV in the US. We visualize the estimated smooth effects to provide new insights into how advertising, demographic variables and TV viewing behavior influence consumer behavior. The predictive performance only drops slightly compared to a competitive benchmark, while interpretation is greatly improved.