Binary geometric process model for the modeling of longitudinal binary data with trend

We propose the Binary Geometric Process (BGP) model for longitudinal binary data with trends. The Geometric Process (GP) model contains two components to capture the dynamics on a trend: the mean of an underlying renewal process and the ratio which measures the direction and strength of the trend. The GP model is extended to binary data using a latent GP. The statistical inference for the BGP models is conducted using the least-square, maximum likelihood (ML) and Bayesian methods. The model is demonstrated through simulation studies and real data analyzes. Results reveal that all estimators perform satisfactorily and that the ML estimator performs the best. Moreover the BGP model is better than the ordinary logistic regression model.