Binary functional linear models under choice-based sampling

A functional binary choice model is explored in a case-control or choice-based sample design context. That is, a model is considered in which the response is binary, the explanatory variable is functional, and the sample is stratified with respect to the values of the response variable. A dimensional reduction of the space of the explanatory random function based on a Karhunen-Loève expansion is used to define a conditional maximum likelihood estimate of the model. Based on this formulation, several asymptotic properties are given. A simulation study and an application to kneading data are used to compare the proposed method with the ordinary maximum likelihood method, which ignores the nature of the sampling. The proposed model yields encouraging results. The potential of the functional choice-based sampling model for integrating special non-random features of the sample, which would have been difficult to see otherwise, is also outlined.