Transform response for hurdle model I am using a hurdle model (dist=negbin, link = logit) for a dataset with multiple explanatory variables, excessive zeros and overdispersion by both, zeros and count data. 
The residual plots (pearson residuals against fitted values) are not very pleasing, datapoints are mostly clustered in the bottom left corner, so I tried transforming the response. Square root transformation led to much "better" residual plots.  I have read, that count data should not be transformed, but this was with reference to glm models. But would it be an appropriate approach when using a hurdle model?



 A: The hurdle (and zero-inflation) count regression models typically use a log-link for the count component of the model. So you already have a log-linear relationship between the expectation of the (latent) count component and the regressors already. Hence, further transformations are usually not necessary/applicable.
Furthermore, a sqrt-transformation of the response does not yield count data anymore, hence this does not make much sense for count data.
I see three possible actions for you:


*

*Do not look at just the residuals but also compare observed and expected frequencies for 0, 1, 2, ... counts. Often the fitted distribution is quite satisfactory even if the residuals are large - especially when the overdispersion is substantial (i.e., low theta in the negbin distribution).

*You have to consider either a different count distribution and/or improve the specification of the regressors in your model to obtain a better fit.

*If your counts are large enough, it may be possible to use a continuous rather than a discrete distribution. Thus, instead of the zero-truncated negative binomial distribution, you could use a zero-truncated normal distribution - either for the original response or after a possible sqrt-transformation etc.


Which of these is most appropriate depends on your data, sample size, and the kind of predictions you want to make.
