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The study of how the number of spikes in a middle temporal visual area (MT/V5) neuron is tuned to the direction of a visual stimulus has attracted considerable attention over the years, but recent studies suggest that the variability of the number of spikes might also be influenced by the directional stimulus. This entails that Poisson regression models are not adequate for this type of data, as the observations usually present over/underdispersion (or both) with respect to the Poisson distribution. This paper makes use of the double exponential family and presents a flexible model to estimate, jointly, the mean and dispersion functions, accounting for the effect of a circular covariate. The empirical performance of the proposal is explored via simulations and an application to a neurological data set is shown.

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