We propose an alternative to the method of generalized estimating equations (GEE) for inference about binary longitudinal data. Unlike GEE, the method is practicable when the data consist of long time series on each subject and the set of observation times is not necessarily common to all subjects. Instead of modelling the intra-series correlations explicitly, we assume that a subject's propensity to respond is governed by an underlying, but unobserved, stationary continuous process. Given a realization of this process, we assume that the binary responses are conditionally independent, with the probability that a subject responds positively at any given time t depending on the value of the underlying process at that time and also on any covariates specific to the subject at that time. We develop an algorithm for estimating the parameters in this model, and investigate its effectiveness using simulation methods. We also apply the methodology to data collected in a trial investigating the effect of self-measurement of blood pressure on compliance in taking medication during a course of anti-hypertension treatment.