Likelihood analysis of latent functional response regression models for sequences of correlated binary data

In this article, 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. Our proposal relies on the use of a complete data likelihood which can 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 estimates of functional regression coefficients and principal components are provided by introducing a novel adaptive EM algorithm. 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. Supporting Information for this article are available online.