  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.
