[R] Can't find all levels of categorical predictors in output of zeroinfl()

[Achim Zeileis]

On Sun, 4 Mar 2012, j.straka wrote:

> Hello,
> I?m using zero-inflated Poisson regression via the zeroinfl() function to
> analyze data on seed-set of plants, but for some reason, I don?t seem to be
> getting the output for all three levels of my two categorical predictors. 
>
> More about my data and model:
> My response variable is the number of viable seeds (AVInt), and my two
> categorical predictors are elevation (Elev) and Treatment (Treatment).  Elev
> has three levels: 01-Low, 02-Mid, and 03-High; Treatment also has three
> possibilities: B, F, or O. 
>
> Because the response variable (AVInt) is zero-inflated and
> Poisson-distributed, I?m using zeroinfl() under the pcsl library as an
> alternative to factorial ANOVA (I?ve also tried the zero-inflated negative
> binomial).  This is early in my data-analysis, but I will likely incorporate
> additional categorical and continuous predictors at a later time. 
>
> This gives me the following model:
>
> zipclay=zeroinfl(AVInt ~ Elev + Treatment)
>
> So running the model, I have: 
>> zipclay=zeroinfl(AVInt ~ Elev + Treatment)
>> summary(zipclay)
>
> Call:
> zeroinfl(formula = AVInt ~ Elev + Treatment)
>
> Pearson residuals:
>    Min      1Q  Median      3Q     Max 
> -1.1958 -0.5612 -0.3764  0.2704  5.5130 
>
> Count model coefficients (poisson with log link):
>            Estimate Std. Error z value Pr(>|z|) 
> (Intercept)  -0.2035     0.3435  -0.592  0.55368 
> Elev02-Mid    0.3937     0.1806   2.180  0.02923 * 
> Elev03-High   0.1635     0.1792   0.912  0.36159 
> TreatmentF    1.0026     0.3305   3.033  0.00242 **
> TreatmentO    0.5915     0.3293   1.796  0.07244 . 
>
> Zero-inflation model coefficients (binomial with logit link):
>            Estimate Std. Error z value Pr(>|z|) 
> (Intercept)   1.6086     0.5080   3.167  0.00154 ** 
> Elev02-Mid   -0.3813     0.4345  -0.878  0.38020 
> Elev03-High  -0.9512     0.4532  -2.099  0.03584 * 
> TreatmentF   -0.9774     0.4690  -2.084  0.03718 * 
> TreatmentO   -3.0242     0.6561  -4.609 4.05e-06 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
>
> Number of iterations in BFGS optimization: 16 
> Log-likelihood: -363.2 on 10 Df
>
> So my question is, where did my "Elev01-Low" and "TreatmentB" go??  Why
> aren't they appearing in the output table?

Both factors are coded with treatment contrasts and hence the main effect 
of the first category is constrained to zero to make the model 
identifiable. But this is the same as in a 2-way ANOVA. Compare with:

   summary(lm(AVInt ~ Elev + Treatment))

where the intercept corresponds to the mean for Elev01-Low/TreatmentB.

The regressors in the zero-inflated models are set up in exactly the same 
way as in such a 2-way ANOVA.

hth,
Z

> Any insight would be greatly appreciated!
>
> - Jason
>
>
>
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