A Unified Neural Network Framework for Extended Redundancy Analysis

Component-based approaches have been regarded as a tool for dimension reduction to predict outcomes from observed variables in regression applications. Extended redundancy analysis (ERA) is one such component-based approach which reduces predictors to components explaining maximum variance in the outcome variables. In many instances, ERA can be extended to capture nonlinearity and interactions between observed and components, but only by specifying a priori functional form. Meanwhile, machine learning methods like neural networks are typically used in a data-driven manner to capture nonlinearity without specifying the exact functional form. In this paper, we introduce a new method that integrates neural networks algorithms into the framework of ERA, called NN-ERA, to capture any non-specified nonlinear relationships among multiple sets of observed variables for constructing components. Simulations and empirical datasets are used to demonstrate the usefulness of NN-ERA. The conclusion is that in social science datasets with unstructured data, where we expect nonlinear relationships that cannot be specified a priori, NN-ERA with its neural network algorithmic structure can serve as a useful tool to specify and test models otherwise not captured by the conventional component-based models.