MAXIMUM LIKELIHOOD ESTIMATION FOR SIMPLEX DISTRIBUTION NONLINEAR MIXED MODELS VIA THE STOCHASTIC APPROXIMATION ALGORITHM

摘要

Longitudinal continuous proportional data is common in many fields such as biomedical research, psychological research and so on, e.g., the percent decrease in glomerular filtration rate at different follow-up times from the baseline. As shown in Song and Tan [16] such data can be fitted with simplex models. However, the original models of [16] for such longitudinal continuous proportional data assumed a fixed effect for every subject. This paper extends the models of Song and Tan [16] by adding random effects, and proposes simplex distribution nonlinear mixed models which are one kind of nonlinear reproductive dispersion mixed model. By treating random effects in the models as hypothetical missing data and applying the Metropolis-Hastings (M-H) algorithm, this paper develops the stochastic approximation (SA) algorithm with Markov chain Monte-Carlo (MCMC) method for maximum likelihood estimation in the models. Finally, for ease of comparison, the method is illustrated with the same data from an ophthalmology study on the use of intraocular gas in retinal surgeries in [16].