Comparison of spatial linear mixed models for ecological data based on the correct classification rates

Abstract

In this paper, a novel approach to comparison and selection of spatial linear mixed models based on a hybrid estimator of actual correct classification rates is considered. We focus on the method of statistical classification based on Bayes discriminant function (BDF) by providing modified well-known methods for estimation of correct classification rates. The proposed approach is illustrated on ecological, spatially distributed data and allows comparing various spatial linear mixed models. Assuming that spatial data follow Gaussian random field (GRF) model, the problem of classifying its observation into one of two populations is considered. The populations are specified by the common linear regressors but different values of regression parameters. Authors concern with classification procedures associated with BDF and its sample version (SDF). SDF is built by replacing the unknown parameters in BDF with their maximum likelihood estimators obtained from the training sample. Two estimators of the actual correct classification rates, i.e., the plug-in and the apparent correct classification rates are considered as estimators of performance measures of classifier based on SDF. A hybrid estimator of the actual correct classification rate, obtained by averaging the mentioned above estimators, is used as the main criterion for model selection. Different types of spatial data models for invasive species (zebra mussels), distributed in the Curonian Lagoon, are compared by the defined criterion. The advantage of the proposed approach against indicator kriging method is shown. Selected spatial models can aid in the mapping of the presence and absence of zebra mussels in the Curonian Lagoon.