Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)

Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η0α0⊤X+β0⊤Z , where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology.

Deep Learning: A Primer for Psychologists

Deep learning has revolutionized predictive modeling in topics such as computer vision and natural language processing but is not commonly applied to psychological data. In an effort to bring the benefits of deep learning to psychologists, we provide an overview of deep learning for researchers who have a working knowledge of linear regression. We first discuss several benefits of the deep learning approach to predictive modeling. We then present three basic deep learning models that generalize linear regression: The feedforward neural network (FNN), the recurrent neural network (RNN), and the convolutional neural network (CNN). We include concrete toy examples with R code to demonstrate how each model may be applied to answer prediction-focused research questions using common data types collected by psychologists.