Sample-based Maximum Likelihood Estimation of the Autologistic Model

Area of Science:

• Spatial statistics
• Statistical modeling
• Computational statistics

Background:

• Autologistic models are widely used for analyzing spatial binary data.
• Estimating parameters for these models, especially on large lattices, is computationally intensive.
• Maximum likelihood estimation (MLE) has been challenging due to the difficulty in computing the normalizing constant.

Purpose of the Study:

• To introduce and evaluate new recursive algorithms for fast computation of the normalizing constant in autologistic models.
• To assess the feasibility and accuracy of sample-based MLE for autologistic parameters.
• To compare sample-based MLE estimates with benchmark estimates and analyze their properties.

Main Methods:

• Development of recursive algorithms for normalizing constant computation.
• Simulation studies using 12 binary lattices (420x420) with varying plot sizes and sample sizes (20-600).
• Comparison of sample-based MLE estimates with Markov Chain Monte Carlo (MCMC) benchmark estimates.

Main Results:

• Sample-based MLE is feasible and provides estimates with a systematic bias of 3%-7%, reducible by calibration.
• Sampling variances of MLE estimates are generally large and conservative.
• The variance for the spatial association parameter is substantially higher (2-10x) than for the abundance parameter.
• Estimate distributions were predominantly non-normal.

Conclusions:

• Sample-based MLE, with appropriate sample size and post-estimation calibration, yields acceptable estimates for autologistic parameters.
• The developed algorithms significantly improve the computational feasibility of parameter estimation.
• Equations for predicting expected sampling variance are provided, aiding in study design and interpretation.