[R] Interpreting the results of the zero inflated negative binomial regression

[Ben Bolker]

Vishnu B <vishnub87 <at> gmail.com> writes:

> I am new to R and has been depending mostly on the online tutotials to learn
> R. I have to deal with zero inflated negative binomial distribution. I am
> however unable to understand the following example from this link
> http://www.ats.ucla.edu/stat/r/dae/zinbreg.htm
> 
> The result gives two blocks.
> 
> *library(pscl)
> zinb<-zeroinfl(count ~ child + camper | persons, dist = "negbin", EM = TRUE)
> summary(zinb)
> 	*Call:
> zeroinfl(formula = count ~ child + camper | persons, dist = "negbin",
>     EM = TRUE)
> 
> Count model coefficients (negbin with log link):
>             Estimate Std. Error z value Pr(>|z|)
> (Intercept)   1.3711     0.2561   5.353 8.63e-08 ***
> child        -1.5152     0.1956  -7.747 9.42e-15 ***
> camper        0.8790     0.2693   3.264  0.00110 **
> Log(theta)   -0.9854     0.1759  -5.601 2.14e-08 ***
> 
> Zero-inflation model coefficients (binomial with logit link):
>             Estimate Std. Error z value Pr(>|z|)
> (Intercept)   1.6028     0.8363   1.917   0.0553 .
> persons      -1.6662     0.6789  -2.454   0.0141 *
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> Theta = 0.3733
> Number of iterations in BFGS optimization: 2
> Log-likelihood: -432.9 on 6 Df
> 
> What does this mean? What is the significance of "| persons" in the example?
> Is the complete summary the full model? When I tried to use it, I got an
> independent variable, which had a z- value of 0.005 in the second block. How
> should i infer?
> 

  You should carefully read the help page for the function you
are using: ?zeroinfl.  The variables on the right hand side of
the bar are the predictor variables for the zero-inflation part
of the model (as the summary suggests).  The p-value (sic) of
0.0553 for the intercept of the zero-inflation component means
that you could reject the null hypothesis that the intercept is
zero (or equivalent that the zero-inflation probability is 0.5
for the baseline level of "persons" (i.e. there were no people
in the camping group -- a somewhat unrealistic baseline level!)


  If you have a predictor variable (not just the intercept)
with a (sic) p-value of 0.005, it means that you can reject
the null hypothesis that the predictor has zero effect on the
zero-inflation component of the model.

  The r-help list is really intended for R questions, and this
verges on a statistics question.  Please read the posting guide ...