Latent function-on-scalar regression models for observed sequences of binary data: a restricted likelihood approach

Abstract: In this paper, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational framework for maximum likelihood analysis via the parameter expansion technique. Compared to existing methods, our proposal relies on the use of a complete data likelihood, with the advantage of being able to handle non-equally spaced and missing observations effectively. The proposed method is used in the Function-on-Scalar regression setting, with the latent response variable being a Gaussian random element taking values in a separable Hilbert space. Smooth estimations of functional regression coefficients and principal components are provided by introducing an adaptive MCEM algorithm that circumvents selecting the smoothing parameters. Finally, the performance of our novel method is demonstrated by various simulation studies and on a real case study. The proposed method is implemented in the R package dfrr.