Approximate maximum likelihood estimation of the autologistic model

Abstract

Approximate Maximum Likelihood Estimation (AMLE) is a simple and general method recently proposed for approximating MLEs without evaluating the likelihood function. The only requirement is the ability to simulate the model to be estimated. Thus, the method is quite appealing for spatial models because it does not require evaluation of the normalizing constant, which is often computationally intractable. An AMLE-based algorithm for parameter estimation of the autologistic model is proposed. The impact of the numerical choice of the input parameters of the algorithm is studied by means of extensive simulation experiments, and the outcomes are compared to existing approaches. AMLE is much more precise, in terms of Mean-Square-Error, with respect to Maximum pseudo-likelihood, and comparable to ML-type methods. Although the computing time is non-negligible, the implementation is straightforward and the convergence conditions are weak in most practically relevant cases.