I am using PROC COUNTREG to look at time trends in fish capture data. As I really don’t expect the fish counts to be from a Poisson distribution, I request the regression to consider the counts as negative binomial variates. PROC COUNTREG offers two ways to relate the variance to the mean when doing negative binomial regression. Either σ 2 = µ + α 2 µ 2 , in which case, observations with mean µ are assumed to follow the distribution (Eq. 1): P(x=m) = PDF(“NEGB”, m, α 2 µ/(1+ α 2 µ), 1/α 2 ), or σ 2 =µ + α 1 µ, which implies the distribution (Eq. 2): P(x=m) = PDF(“NEGB”, m, α 1 /(1+ α 1 ), µ/α 1 ). (I added a subscript to alpha because both values are not, and should not be, the same) I wanted to compare the fit of both alternatives to my data. I was able to generate a confidence interval around the fitted curves using Eq. 1, but when tried to do the same with Eq. 2, the values made no sense. I would like to know: what does the estimated parameter _Alpha, as reported in the OUTEST= dataset, represent when DIST=NEGBIN(P=1) is requested? PG
... View more