Repeated measures in functional logistic regression

We present a proposal to extend the functional logistic regression model –which models a binary scalar response variable from a functional predictor– to the case where the functional observations are not independent because the same functional variable is measured in the same individuals in different experimental conditions (repeated measures). The extension is addressed by including a random effect in the model. The functional approach of this model assumes that all functional objects are elements of the same finite-dimensional subspace of the space of square-integrable functions L2 in the same compact domain allowing the functions to be treated through the basis coefficients on the basis that generates the subspace to which functional objects belong (basis expansion). This methodology usually induces a multicollinearity problem in the multivariate model that emerges, which is solved with the use of the functional principal components of the functional predictor, resulting in a new functional principal component random effects model. The proposal is contextualized through a simulation study that contains three simulation scenarios for four different functional parameters and considering the lack of independence.