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In this paper, we study a functional regression setting where the randomresponse curve is unobserved, and only its dichotomized version observed at asequence of correlated binary data is available. We propose a practicalcomputational framework for maximum likelihood analysis via the parameterexpansion technique. Compared to existing methods, our proposal relies on theuse of a complete data likelihood, with the advantage of being able to handlenon-equally spaced and missing observations effectively. The proposed method isused in the Function-on-Scalar regression setting, with the latent responsevariable being a Gaussian random element taking values in a separable Hilbertspace. Smooth estimations of functional regression coefficients and principalcomponents are provided by introducing an adaptive MCEM algorithm thatcircumvents selecting the smoothing parameters. Finally, the performance of ournovel method is demonstrated by various simulation studies and on a real casestudy. The proposed method is implemented in the R package dfrr.

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