Hierarchical neural networks for clustered regression analysis: an application to income data in canada

In the context of regression analysis, neural networks are often useful when there is uncertainty in the mean response structure or deviation from standard distributional assumptions. In this paper, we present a hierarchical neural network framework for regression analysis of clustered correlated data and investigate its predictive performance relative to the classical linear mixed model.

Specifically, we examine how the neural network compares to commonly used linear mixed models for analyzing clustered correlated or repeated measures data under various types of model misspecifications, including nonlinearity in the mean response function and outliers in the response variable. To handle outliers, we use a Huber-type loss function when predicting outcomes with the neural network. The performance of the neural network is studied through a simulation.