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I'm trying to build ZINB and hurdle NB models for my data. Everything seems reasonable, but I have some problems by understanding some problems.

1.One of regressors,which should be reasonable gives NA values in models summary in both parts in the model,thought all other regressors seems significant and clear. I tried to put offset(sent) or offset(log(sent)) or offset = sent, but it not helps. In first two ways it gives an error : no valid set of coefficients has been found: please supply starting values . That regressor is integer. Does anyone know the way that I could fix this problem? (All criteria shows better model with that regressor in the model).

                                     Estimate Std. Error z value Pr(>|z|)    

Sent                                  2.048e-05         NA      NA       NA 
 Warning message:
 In sqrt(diag(object$vcov)) : NaNs produced

2.Is it possible to check the deviance in ZINB and hurdle models? Because in simple NB function deviance() works well and in ZINB it gives NULL. How should I interpret this thing?

3.To find the best model I'm using Vuong criteria, LR test,AIC. Is there some better criteria for models comparison? How to check and interprete residuals for zero-inflated models ?

4.Is it right that for regressor estimates I should use exp(Estimates), not just simple coefficients? Is it the same for both ZINB and hurdle models?

I hope my problems are clear, it's little hard to understand those two models for my, so I really hope for help. Thank you in advance !

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