  Generalized Linear Models (GLMs) have been used extensively in statistical
models of spike train data. However, the IRLS algorithm, which is often used to
fit such models, can fail to converge in situations where response and
non-response can be separated by a single predictor or a linear combination of
multiple predictors. Such situations are likely to arise in many neural systems
due to properties such as refractoriness and incomplete sampling of the signals
that influence spiking. In this paper, we describe multiple classes of
approaches to address this problem: Standard IRLS with a fixed iteration limit,
computing the maximum likelihood solution in the limit, Bayesian estimation,
regularization, change of basis, and modifying the search parameters. We
demonstrate a specific application of each of these methods to spiking data
from rat somatosensory cortex and discuss the advantages and disadvantages of
each. We also provide an example of a roadmap for selecting a method based on
the problem's particular analysis issues and scientific goals.
