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

Fatemeh Asgari, Mohammad H. Alamatsaz, Saeed Hayati and Valeria Vitelli

Scandinavian Journal of Statistics, 2025, vol. 52, issue 2, 840-872

Abstract: 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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:52:y:2025:i:2:p:840-872

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