R help - Aug 2013 - Problem with zero-inflated negative binomial model in sediment river dynamics

Dear All,

I am running a negative binomial model in R using the package pscl in oder to
estimate bed sediment movements versus river discharge. Currently we have
deployed 4 different plates to test if a combination of more than one plate
would better describe the sediment movements when the river discharge changes
over time.

My data are positively skewed and zero-inflated. I did run both zero-inflated
Poisson and zero-inflated negative binomial regression and compared them using
the VUONG test which showed that the negative binomial works better than a
simple zero-inflated Poisson.

My models look like:


1) plate1 ~ river discharge
2) (plate 1 + plate 2) ~ river discharge
3) (plate 1 + plate 2 +plate 3) ~ river discharge
4) (plate 1 + plate 2 + plate 3 + plate 4) ~ river discharge


My main problem as I am new to these type of models is that I get a different
sign for the coefficent of discharge in the output of the zero-inflated negative
binomial model (please see below). What does this mean? Also how could I compare
the different models (1-4) i.e. what tells me which is performing best? Thank
you very much in advance for any comments and suggestions!!

Kind Regards,
Valentina


Call:
zeroinfl(formula = plate1 ~ discharge, data = datafit_plates, dist =
"negbin", EM = TRUE)
Pearson residuals:
    Min      1Q  Median      3Q     Max
-0.6770 -0.3564 -0.2101 -0.0814 12.3421

Count model coefficients (negbin with log link):
                         Estimate    Std. Error z value Pr(>|z|)
(Intercept)  2.557066     0.036593   69.88   <2e-16 ***
discharge    0.064698    0.001983   32.63   <2e-16 ***
Log(theta)  -0.775736   0.012451  -62.30   <2e-16 ***

Zero-inflation model coefficients (binomial with logit link):
                      Estimate    Std. Error     z value    Pr(>|z|)
(Intercept)   13.01011    0.22602      57.56   <2e-16 ***
discharge    -1.64293    0.03092       -53.14   <2e-16 ***
Theta = 0.4604
Number of iterations in BFGS optimization: 1
Log-likelihood: -6.933e+04 on 5 Df






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Lauria:  For historical reasons the logistic regression (binomial with
logit link) model portion of a zero-inflated count model is usually
structured to predict the probability of the 0 counts rather than the
nonzero (>=1) counts so the coefficients will be the negative of what you
expect based on the count model portion (as in your output).  It is simple
to interpret the probability of the logistic regression portion as the
probability of the nonzero counts by just taking the negative of the
coefficient estimates provided for the probability of the zero counts.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  cadeb@usgs.gov <brian_cade@usgs.gov>
tel:  970 226-9326



On Tue, Aug 13, 2013 at 9:06 AM, Lauria, Valentina <
valentina.lauria@nuigalway.ie> wrote:
> Dear All,
>
> I am running a negative binomial model in R using the package pscl in oder
> to estimate bed sediment movements versus river discharge. Currently we
> have deployed 4 different plates to test if a combination of more than one
> plate would better describe the sediment movements when the river discharge
> changes over time.
>
> My data are positively skewed and zero-inflated. I did run both
> zero-inflated Poisson and zero-inflated negative binomial regression and
> compared them using the VUONG test which showed that the negative binomial
> works better than a simple zero-inflated Poisson.
>
> My models look like:
>
>
> 1) plate1 ~ river discharge
> 2) (plate 1 + plate 2) ~ river discharge
> 3) (plate 1 + plate 2 +plate 3) ~ river discharge
> 4) (plate 1 + plate 2 + plate 3 + plate 4) ~ river discharge
>
>
> My main problem as I am new to these type of models is that I get a
> different sign for the coefficent of discharge in the output of the
> zero-inflated negative binomial model (please see below). What does this
> mean? Also how could I compare the different models (1-4) i.e. what tells
> me which is performing best? Thank you very much in advance for any
> comments and suggestions!!
>
> Kind Regards,
> Valentina
>
>
> Call:
> zeroinfl(formula = plate1 ~ discharge, data = datafit_plates, dist >
"negbin", EM = TRUE)
> Pearson residuals:
>     Min      1Q  Median      3Q     Max
> -0.6770 -0.3564 -0.2101 -0.0814 12.3421
>
> Count model coefficients (negbin with log link):
>                          Estimate    Std. Error z value Pr(>|z|)
> (Intercept)  2.557066     0.036593   69.88   <2e-16 ***
> discharge    0.064698    0.001983   32.63   <2e-16 ***
> Log(theta)  -0.775736   0.012451  -62.30   <2e-16 ***
>
> Zero-inflation model coefficients (binomial with logit link):
>                       Estimate    Std. Error     z value    Pr(>|z|)
> (Intercept)   13.01011    0.22602      57.56   <2e-16 ***
> discharge    -1.64293    0.03092       -53.14   <2e-16 ***
> Theta = 0.4604
> Number of iterations in BFGS optimization: 1
> Log-likelihood: -6.933e+04 on 5 Df
>
>
>
>
>
>
>         [[alternative HTML version deleted]]
>
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