Regression models for binary time series with gaps

Time series of discrete random variables present unique statistical challenges due to serial correlation and uneven sampling intervals. While regression models for a series of counts are well developed, only few methods are discussed for the analysis of moderate to long (e.g. from 20 to 152 observations) binary or binomial time series. This article suggests generalized linear mixed models with autocorrelated random effects for a parameter driven approach to such series. We use a Monte Carlo EM algorithm to jointly obtain maximum likelihood estimates of regression parameters and variance components. The likelihood approach, although computationally extensive, allows estimation of marginal joint probabilities of two or more serial events. These are crucial in checking the goodness of fit, whether the model adequately captures the serial correlation and for predicting future responses. The model is flexible enough to allow for missing observations or unequally spaced time intervals. We illustrate our approach and model assessment tools with an analysis of the series of winners in the traditional boat race between the universities of Oxford and Cambridge, re-evaluating a long-held belief about the effect of the weight of the crew on the odds of winning. We also show how our methods are useful in modeling trends based on the General Social Survey database.