A method for bias-reduction of sample-based MLE of the autologistic model

Sample-based maximum likelihood estimates (MLEI) of the autologistic function parameters obtained from a one-stage simple random cluster sample from a finite population of binary units on a regular grid are biased due to the neglected association between population units across cluster boundaries. This is because such estimates are based on the autologistic lattice of size corresponding to the sample cluster rather than that of the overall grid of interest. Considering a buffer of one row (column) of units around each sample cluster with ‘missing data’ and assuming independence of these buffered clusters permits a new set of maximum likelihood estimates (MLEB) after integrating out the missing data in the likelihood. MLEB are much less biased than MLEI and have much smaller root mean square errors. In a simulation study with square regular clusters with m={4,5,6,7}m={4,5,6,7} rows (columns) of units, sample sizes n={50,100,200}n={50,100,200}, and nine 420×420 spatial fields with known values of the autologistic model parameters the buffering eliminated about 75% of the bias in MLEI and reduced root mean square errors accordingly. Achieved MLEB coverage rates of 95% confidence intervals were slightly conservative. We recommend buffering since it is easy to implement without adding significantly to computational efforts.