Scalar-on-density regression with sparsely observed densities

Feeser Johannes, Humboldt-Universität zu Berlin

Co-authors: Sonja Greven, Humboldt-Universität zu Berlin

Abstract: We present a method to estimate linear functional regression models for scalar outcomes with a sparsely observed density-valued regressor. The regression model includes the Bayes Hilbert space inner product of the latent density with a functional (density-valued) coefficient. For estimation, we use a Monte-Carlo Expectation-Maximization (MCEM) algorithm. The centered log-ratio (clr) transformations of latent regressor densities are described as realizations of a finite-dimensional Gaussian process, and the functional regression coefficient is represented using an appropriate spline basis.

In our application, we test for the presence of peer effects in education via covariate test score densities in school classes using data from the Student Teacher Achievement Ratio (STAR) study.