The authors consider regression analysis for binary data collected repeatedly over time on members of numerous small clusters of individuals sharing a common random effect that induces dependence among them. They propose a mixed model that can accommodate both these structural and longitudinal dependencies. They estimate the parameters of the model consistently and efficiently using generalized estimating equations. They show through simulations that their approach yields significant gains in mean squared error when estimating the random effects variance and the longitudinal correlations, while providing estimates of the fixed effects that are just as precise as under a generalized penalized quasi-likelihood approach. Their method is illustrated using smoking prevention data.

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Keywords Cluster-correlated data, Logistic regression, Random effects, Simulated quasi-likelihood
Journal Canadian Journal of Statistics
Sutradhar, B.C. (Brajendra C.), & Farrell, P. (2004). Analyzing multivariate longitudinal binary data: A generalized estimating equations approach. Canadian Journal of Statistics, 32(1), 39–55.