PROC GENMOD Negative Binomial doesn't predict zeros I am using PROC GENMOD with time series data, I have tried to work with Negative Binomial, Poisson, GEE and Zero Inflated Poisson, but in each case when I score my validation dataset, I am getting predicted values which are never zero.
E.g. A customer might buy fuel every 4 weeks, the model does not predict the weeks in between fuel fills as zeros.
Is there a better way of predicting the weeks with zero fuel fills? I assumed Negative Binomial would be able to do this, but the lack of predicted zero outcomes, which represent 78% of the fuel filling weeks (by customer) has made this model ineffective.
Thanks in advance!!
 A: Let $Y$ be response variable, $X$ be the covariate.
When we fit the model, we are try to find the conditional distribution of $Y$ conditional on $X$.
Here we use Poisson regression as example .
When we fit the Poisson regression, we assume that $Y$ follows Poisson distribution for the given $X$.
$$\Pr(Y=y|X=x) = \frac {e^{-\lambda(x)}\lambda(x)^y}{y!}$$
Then we assume that $\log(\lambda(x))=\beta_0+\beta_1x$. In the process of model fitting, $\beta_0$ and $\beta_1$ were estimated.
After we get the estimate of $\beta_0$ and $\beta_1$, we have the conditional distribution of $Y$. From the known distribution, we can calculate the probability of $Y=0, 1, ...$.
So model provides the conditional distribution of response variable, not the prediction of the response variable. 
After model fitting, software generally also provides the mean of the response variable based on the conditional distribution. For Poisson regression, $\exp(\hat \beta_0 + \hat \beta_1x)$ is provided. But it will not be zero. This is the reason why you do not get the "predicted" values being zero.   
