A little more.
As Christopher Ryan points out, as long as the zero-inflation model
is non-trivial (i.e. more complex than a single intercept for the whole
population), there's a pi(i) for every observation i (you could
certainly average the pi(i) values if you wanted, or compute pi for an
averaged set of covariates).
library(pscl)
fm_zinb2 <- zeroinfl(art ~ . | ., data = bioChemists, dist = "poisson")
pi_i <- predict(fm_zinb2, type = "zero")
head(pi_i)
## 1 2 3 4 5 6
## 0.13392803 0.21936320 0.21973454 0.24697313 0.01890023 0.34281196
To get the conditional probability that a zero observation is a
structural or a sampling zero, compute the probability of a sampling
zero (exp(-mu[i]) for a Poisson model) and use Bayes' rule, assuming
equal prior probs
## probability of _sampling_ zero
psampz <- exp(-predict(fm_zinb2, type = "count"))
head(psampz)
## 1 2 3 4 5 6
## 0.09507376 0.18361241 0.18688646 0.14774602 0.08992667 0.27235498
pz <- 1 - (1-pi_i)*(1-psampz) ## prob of zero of either type
## 1 2 3 4 5 6
## 0.2162687 0.3626978 0.3655556 0.3582299 0.1071273 0.5218004
psampz/pz
head(psampz)/head(pz)
## 1 2 3 4 5 6
## 0.4396093 0.5062408 0.5112395 0.4124336 0.8394378 0.5219524
3. I'm not aware of a closed-form solution for zero-inflation models
as long as the count and/or structural-zero components depend on
covariates? In any case, looking inside zeroinfl() you can see that it
calls optim() [using BFGS by default, see ?pscl::zeroinfl.control]
cheers
Ben Bolker
On 2024-01-04 9:38 a.m., Christopher W. Ryan via R-help wrote:
Are you referring to the zeroinfl() function in the countreg package? If
so, I think
predict(fm_zinb2, type = "zero", newdata = some.new.data)
will give you pi for each combination of covariate values that you
provide in some.new.data
where pi is the probability to observe a zero from the point mass component.
As to your second question, I'm not sure that's possible, for any
*particular, individual* subject. Others will undoubtedly know better
than I.
--Chris Ryan
Sorkin, John wrote:
I am running a zero inflated regression using the zeroinfl function similar to
the model below:
fm_zinb2 <- zeroinfl(art ~ . | ., data = bioChemists, dist = "poisson")
summary(fm_zinb2)
I have three questions:
1) How can I obtain a value for the parameter pie, which is the fraction of the
population that is in the zero inflated model vs the fraction in the count
model?
2) For any particular subject, how can I determine if the subject is in the
portion of the population that contributes a zero count because the subject is
in the group of subjects who have structural zero responses vs. the subject
being in the portion of the population who can contribute a zero or a non-zero
response?
3) zero inflated models can be solved using closed form solutions, or using
iterative methods. Which method is used by fm_zinb2?
Thank you,
John
John David Sorkin M.D., Ph.D.
Professor of Medicine, University of Maryland School of Medicine;
Associate Director for Biostatistics and Informatics, Baltimore VA Medical
Center Geriatrics Research, Education, and Clinical Center;
PI Biostatistics and Informatics Core, University of Maryland School of
Medicine Claude D. Pepper Older Americans Independence Center;
Senior Statistician University of Maryland Center for Vascular Research;
Division of Gerontology and Paliative Care,
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
Cell phone 443-418-5382
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