Joint generalized estimating equations for longitudinal binary data

Modeling longitudinal binary data is challenging but common in practice. Existing methods on modeling of responses take no account the fact that correlation coefficient must have an upper bound which smaller than one. Ignoring this can lead to incorrect statistical inferences for data. A novel method proposed model mean and within-subject coefficients data, simultaneously, by taking into constraints bounds. By introducing latent normally distributed random variables, are connected those modeled accordingly. joint generalized estimating equation (GEE) developed purpose resulting shown satisfy constraints. Asymptotic normality parameter estimators derived simulation studies made under various scenarios, showing GEE works very well even if working covariance structures misspecified. For illustration, applied two real practices assess effects covariates coefficients.