Assessment of Different Link Functions for Modeling Binary Data to Derive Sound Inferences and Predictions

Abstract

Binary data are widely used for spatial modeling and when inferences and predictions are to be derived. If a Generalized Linear Model (GLM) is applied, logit functions are often used. Here we show alternatives to the traditional logit approach using probit and the complementary log log link functions. We present a software-based approach and two methods of assessing which link function performs best for inferences and for predictions. The first decision criterion is centered around the model deviance, e.g. relevant for inferences. The second criterion is based on predicting the findings back to the training data and then using the differences between expected and predicted values for known presences and absences as an indication of the fit. As an example we use Marbled Murrelet (Brachyramphus marmoratus) nesting habitat data derived from aerial telemetry and overlaid with GIS habitat layers (DEM and Forest Cover). This data set is large and carries inherent noise due to field data and a complex landscape; therefore it well covers the extremes of the fitted link functions. It is a representative example for a situation where the selection of a link function could affect the results. Findings indicate that for our data all three link functions behave similar, but logit link functions perform better than the cloclog and probit link functions when inferences as well as predictions are the study goals.