  Generalized Linear Models (GLMs) are an increasingly popular framework for
modeling neural spike trains. They have been linked to the theory of stochastic
point processes and researchers have used this relation to assess
goodness-of-fit using methods from point-process theory, e.g. the
time-rescaling theorem. However, high neural firing rates or coarse
discretization lead to a breakdown of the assumptions necessary for this
connection. Here, we show how goodness-of-fit tests from point-process theory
can still be applied to GLMs by constructing equivalent surrogate point
processes out of time-series observations. Furthermore, two additional tests
based on thinning and complementing point processes are introduced. They
augment the instruments available for checking model adequacy of point
processes as well as discretized models.

Neurons and Cognition