[R-sig-eco] Zero-inflated model inquiry

[Drew Tyre]

Hi Peter,

Your assumption that Before and During are contrasted with After is
correct. By default R parameterizes categorical variables using
treatment contrasts which compare each level to the first one, and the
default sorting is lexicographic, so AFTER becomes the first level.
Your model is indicating that the average abundance both BEFORE and
DURING are significantly different from the AFTER. It sounds like what
you'd like to know is also BEFORE different from DURING. I see a
couple things you could try
1) Make predictions of the average urchin_abundance from the model for
each period along with confidence intervals. Use the confidence
intervals to decide what is the same and different.
2) Change your formula to urchin_density~impact_period-1. This will
give you a distinct estimate for each period, and make construction of
the confidence intervals in 1 very easy, but still won't give you all
the pairwise comparisons.
3) Check the package multcomp and use it to find the appropriate
contrasts for all three levels. I'm not sure this will work for models
from the pscl package.

hth

On Tue, Sep 25, 2012 at 10:50 PM, Peter Houk <peterhouk at gmail.com> wrote:
> 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
>
>         [[alternative HTML version deleted]]
>
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-- 
Drew Tyre

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