Greetings -

I have a question regarding the use of zero-inflated models for count
data.  I have a very basic count dataset consisting of sea urchin density
estimates conducted across 20 sites (random: pooled for this example)
during three timeframes (fixed: 1-before disturbance, 2-during disturbance,
and 3-after disturbance).  For this example, I'm simply looking to
interpret significant differences across timeframes.  After initial
examinations, the data lend themselves well to an overdispersed, negative
binomial distribution (i.e., hurdle approach using the R package pscl).

Using the code:

> f1<-formula(urchin_density~impact_period)
> H1<-hurdle(f1, dist="negbin", link="logit")
> summary(H1)

provides:

Count model coefficients (truncated negbin with log link):
                    Estimate Std. Error z value Pr(>|z|)
(Intercept)           0.7212     0.1546   4.664 3.10e-06 ***
impact_periodBefore   0.6374     0.1713   3.720 0.000199 ***
impact_periodDuring   0.6850     0.1696   4.039 5.37e-05 ***
Log(theta)           -0.6671     0.2262  -2.949 0.003184 **
Zero hurdle model coefficients (binomial with logit link):
                    Estimate Std. Error z value Pr(>|z|)
(Intercept)          0.51904    0.12824   4.048 5.18e-05 ***
impact_periodBefore  0.01869    0.20111   0.093    0.926
impact_periodDuring -0.03353    0.19718  -0.170    0.865
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Theta: count = 0.5132
Number of iterations in BFGS optimization: 11
Log-likelihood: -1377 on 7 Df



Before moving to more complex models, my question is regarding whether or
not this is the right approach, and if so, why are there no results for the
"after" impact period.  My assumption is that both the "before" and
"during" time periods are being contrasted against the "after" here, but
how can one contrast all three groups to look for significance?  Last, how
does one logically translate the two parts of the results?


Insight appreciated, I'm aware there are extensive textbooks on the
subject, but trying to get an initial feel for things.

Peter



-- 
Peter Houk, PhD
Chief Biologist
Pacific Marine Resources Institute
www.pacmares.com
www.micronesianfishing.com

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