Lucia, Your expected values for both the poisson and negative binomial should be positive, because the expected values represent the "rate" at which events occur. But, the coefficients could be negative. Furthermore, the first differences could be negative (one could imagine a treatment decreasing the rate at which events occur). To simulate the uncertainty around our estimates and first differences, we first will want to simulate the coefficients. Take many draws (like, 1000) from a multivariate normal distribution that is centered at our maximum likelihood estimate, with a variance-covariance matrix equal to the negative inverted hessian. Then, we can exploit the simulation shortcut (from Gary's slides) that will allow us to directly calculate the expected value for each distribution (without taking many draws from the predictive distribution for each coefficient simulation). Once you have these calculated, take a simple difference between two simulated expected values to calculate the first differences. You can then characterize the average sized simulation, a 95 percent confidence interval, or standard error using these simulated values. Interestingly, if one were apprehensive about simulating, you could use the delta method to construct approximate confidence bounds. See the notes under the "section" heading, if you are curious This is a great question--if I didn't answer it adequately, let me know and I'll try and explain it differently, or if someone can explain anything I said better please send a post to the list! Cheers! Justin On Wed, 11 Apr 2007, Lucia Tiererova wrote: