A Model for Serial Dependence in Logistic Regression

A model is proposed for binary time series with marginal probabilities given by logistic regression on explanatory variables, by analogy with the first order autoregressive error model for least squares regression. Measurements at adjacent time points are assumed to have an odds ration that is no equal to one and that is constant as a function of time. Measurements separated in time are assumed to be conditionally independent given an intervening observation. Consequences of using and ordinary logistic model in the presence of serial dependence are explored. The closest logistic model, defined as the one with the same marginal probabilities. Consistency of the maximum likelihood estimator of the serial dependence model is proved under certain conditions, and a procedure for finding these estimates is given. Properties of the model are found, including expressions for the joint probabilities and the odds ratio between observations separated in time. The model is shown to generate -mixing processes. A score test is derived in order to test for independence after performing an ordinary logistic regression, and properties of ths test are explored. The effects of missing data on the score test and on estimation of the odds ratio (with known coefficients) are presented. The model is applied to the problem of automatic classification of EKG data based on feature extraction. A positive serial dependence is found in the examples presented. (Author)