BAYESIAN GENERALIZED DISSIMILARITY MODEL: THE POSTERIOR MEAN EXISTENCE AND ITS IMPLEMENTATION ON THE COMMUNITY ECOLOGY ANALYSIS

The Bayesian Generalized Dissimilarity Model (BGDM) is proposed in this paper for estimating the parameters of the Generalized Dissimilarity Model (GDM) using Bayesian approaches. The logit link function is used to estimate the GDM’s response variable, which is characterized as a binomial process. However, the logit function in Generalized Linear Model (GLM) is sensitive to the data separation issue, resulting in the estimator’s non-existence. This research was aimed to assess and evaluate the existence of BGDM estimator (posterior mean) under different prior theoretically and empirically. Parameter estimation of BGDM uses the Hamiltonian Monte Carlo (HMC) technique for carrying out the Markov Chain Monte Carlo (MCMC) approach that required for solving the complex integration in Bayesian procedure. The paper presents theoretical and simulation study results that suggest that the posterior mean can be used as the estimator of the BGDM, regardless of its prior distribution, as long as there is no solitary separator in the data. However, if there is any solitary separator in the data, the posterior mean does not exist under a prior distribution that has an undefined mean. Moreover, BGDM also has better estimation results in modelling community ecology data.