We present a basis solution for the modelling of a binary response with a functional covariate plus any number of scalar covariates. This can be thought of as singular longitudinal data analysis as there are more measurements on the functional covariate than subjects in the study. The maximum likelihood parameter estimates are found using a basis expansion and a modified Fisher scoring algorithm. This technique has been extended to model a functional covariate with a repeated stimulus. We used periodically stimulated foetal heart rate tracings to predict the probability of a high risk birth outcome. It was found that these tracings could predict 94.1 per cent of the high risk pregnancies and without the stimulus, the heart rates were no more predictive than chance.