Gaussian Semiparametric Analysis Using Hierarchical Predictive Models

The Hierarchical Predictive Model (HPM) is a semiparametric mixed model where the fixed effects are fit with a user-specified non-parametric component, allowing for more flexible nonparametric estimation.

Abstract

The Hierarchical Predictive Model (HPM) is a semiparametric mixed model where the fixed effects are fit with a user-specified non-parametric component. This approach extends current spline-based semiparametric mixed model formulations, allowing for more flexible nonparametric estimation. Greater adaptability simplifies model specification making it easier to analyze data sets with large numbers of predictors. Greater automation also extends the scope of exploratory analyses that may be performed with mixed models. Using a HPM, the analyst may select the predictive model to best suit their needs, exploiting the strengths of currently available predictive methods. A simulation study is used to demonstrate the advantages of accounting for known hierarchical structure in predictive models and to illustrate the adaptability of current decision-tree based predictive models. A HPM of the relative abundance of the North American House Finch (Carpodacus mexicanus) is used to demonstrate exploratory analysis with a real data set.