On Wed, 14 Aug 2013, Cade, Brian wrote:
Z is correct, of course. I was just being a little too simplistic in my
explanation trying to emphasize the reversal of signs of the
coefficients in the logistic regression part of the zero-inflated model.
When users ask me what the binary part of the two types of count models
mean, I always say:
- In the zero-inflation model, the binary model predicts the probability
of _zero inflation_ (= excess zeros).
- In the hurdle model, the binary model predicts the probability for
_hurdle crossing_ (= non-zero response).
To me this always seemed natural, even if the sign reversal in the
zero-inflation model may be surprising at first sight...
hth,
Z
Brian
Brian S. Cade, PhD
U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO 80526-8818
email: ca...@usgs.gov
tel: 970 226-9326
On Wed, Aug 14, 2013 at 4:07 AM, Achim Zeileis <achim.zeil...@uibk.ac.at>
wrote:
On Tue, 13 Aug 2013, Cade, Brian wrote:
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.
This is a common misinterpretation but not quite correct.
The zero-inflation model is a mixture model of two components:
(1) a count component (Poisson, NB, ...), and (2) a zero mass
component (i.e., zero with probability 1). Hence, the observed
zeros in the data can come from both sources: either they are
"random" zeros from component (1) or "excess" zeros from
component (2).
The binomial zero-inflation part of the model predicts the
probability that a given observation belongs to component (1).
Thus, the probability of an "excess zero". But this is _not_ the
probability of observing a zero in the data (which is larger
than the excess zero probability).
If you want a model that first models zero vs. non-zero and
second the non-zero counts, use the hurdle model. This has
exactly the interpretation you describe above.
Best,
Z
Brian
Brian S. Cade, PhD
U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO 80526-8818
email: ca...@usgs.gov <brian_c...@usgs.gov>
tel: 970 226-9326
On Tue, Aug 13, 2013 at 9:06 AM, Lauria, Valentina <
valentina.lau...@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
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