A new mixed-effects mixture model for constrained longitudinal data

Biomedical research often features continuous responses bounded by the interval [0, 1]. The well-known beta regression model addresses the constrained nature of these data, while its augmented and mixed-effects variants can address the presence of zeros and/or ones and longitudinal or clustered response values, respectively. However, these models are not robust to the presence of outliers and/or excessive number of observations near the tails. We propose a new augmented mixed-effects regression model based on a special beta mixture distribution that is capable of handling these issues. Extensive simulation studies show the superiority of the proposed model to the models most often used in the literature. The proposed model is applied to two real datasets: one taken from a long-term study of Parkinson's disease and the other taken from a study on reading accuracy.