Using Tweedie distributions for fitting spike count data

Background: The nature of spike count distributions is of great practical concern for the analysis of neural data. These distributions often have a tendency for 'failures' and a long tail of large counts, and may show a strong dependence of variance on the mean. Furthermore, spike count distributions often show multiplicative rather than additive effects of covariates. We analyzed the responses of neurons in primary auditory cortex to transposed stimuli as a function of interaural time differences (ITD). In more than half of the cases, the variance of neuronal responses showed a supralinear dependence on the mean spike count. New method: We explored the use of the Tweedie family of distributions, which has a supralinear dependence of means on variances. To quantify the effects of ITD on neuronal responses, we used generalized linear models (GLMs), and developed methods for significance testing under the Tweedie assumption. Results: We found the Tweedie distribution to be generally a better fit to the data than the Poisson distribution for over-dispersed responses. Comparison with existing methods: Standard analysis of variance wrongly assumes Gaussian distributions with fixed variance and additive effects, but even generalized models under Poisson assumptions may be hampered by the over-dispersion of spike counts. The use of GLMs assuming Tweedie distributions increased the reliability of tests of sensitivity to ITD in our data. Conclusions: When spike count variance depends strongly on the mean, the use of Tweedie distributions for analyzing the data is advised.