Linear scalar-on-surface random effects regression models

Abstract

Many research fields increasingly involve analyzing data of a complex structure. Models investigating the dependence of a response on a predictor have moved beyond the ordinary scalar-on-vector regression. We propose a regression model for a scalar response and a surface (or a bivariate function) predictor. The predictor has a random component and the regression model falls in the framework of linear random effects models. We estimate the model parameters via maximizing the log-likelihood with the ECME (Expectation/Conditional Maximization Either) algorithm. We use the approach to analyze a data set where the response is the neuroticism score and the predictor is the resting-state brain function image. In the simulations we tried, the approach has better performance than two other approaches, a functional principal component regression approach and a smooth scalar-on-image regression approach.