[R] Zero inflated: is there a limit to the level of inflation

[Marc Schwartz]

On Jun 26, 2012, at 2:10 PM, SSimek wrote:

> Hello, 
> 
> I have count data that illustrate the presence or absence of individuals in
> my study population. I created a grid cell across the study area and
> calcuated a count value for each individual per season per year for each
> grid cell. The count value is the number of time an individual was present
> in each grid cell.  For illustration my data columns look something like
> this and are repeated for each individual:
> 
> Cell_ID	Param1	Param2	Param3	Param4	COUNT	Name	Year	Season	Cov
> 1	160.565994	729.08	1503	7930.3	0	AA	2010	AUT	Open
> 1	160.565994	729.08	1503	7930.3	22	AA	2011	SPR	Open
> 1	160.565994	729.08	1503	7930.3	12	AA	2009	SUM	Open
> 1	160.565994	729.08	1503	7930.3	0	AA	2010	SUM	Open
> 2	169.427001	491.87	1503.31	5101.09	0	AA	2010	AUT	oldHard
> 2	169.427001	491.87	1503.31	5101.09	16	AA	2011	SPR	oldHard
> 2	169.427001	491.87	1503.31	5101.09	0	AA	2009	SUM	oldHard
> 2	169.427001	491.87	1503.31	5101.09	0	AA	2010	SUM	oldHard
> …									
> 563	86.777099	612.69	977	4474.6	62	AA	2010	AUT	Water
> 563	86.777099	612.69	977	4474.6	12	AA	2011	SPR	Water
> 563	86.777099	612.69	977	4474.6	55	AA	2009	SUM	Water
> 									
> 									
> 1	160.565994	729.08	1503	7930.3	0	BB	2010	SUM	Open
> 2	169.427001	491.87	1503.31	5101.09	72	BB	2010	SUM	oldHard
> 5	160.75	614.95	1503.31	2878.98	16	BB	2010	SUM	medHard
> 6	170.404998	510.58	1489.44	743.14	0	BB	2010	SUM	Water
> …									
> 563	86.777099	612.69	977	4474.6	0	BB	2010	SUM	Water
> 									
> 									
> 1	160.565994	729.08	1503	7930.3	14	C	2005	AUT	Open
> 1	160.565994	729.08	1503	7930.3	0	C	2006	AUT	Open
> 1	160.565994	729.08	1503	7930.3	0	C	2006	SPR	Open
> 1	160.565994	729.08	1503	7930.3	56	C	2007	SPR	Open
> 1	160.565994	729.08	1503	7930.3	0	C	2006	SUM	Open
> 2	169.427001	491.87	1503.31	5101.09	124	C	2005	AUT	oldHard
> 2	169.427001	491.87	1503.31	5101.09	231	C	2006	AUT	oldHard
> 2	169.427001	491.87	1503.31	5101.09	889	C	2006	SPR	oldHard
> 2	169.427001	491.87	1503.31	5101.09	0	C	2007	SPR	oldHard
> …									
> 563	86.777099		612.69	977	4474.6	0	C	2005	AUT	Water
> 563	86.777099		612.69	977	4474.6	231	C	2006	AUT	Water
> 563	86.777099		612.69	977	4474.6	185	C	2006	SPR	Water
> 563	86.777099		612.69	977	4474.6	123	C	2007	SPR	Water
> 563	86.777099		612.69	977	4474.6	52	C	2006	SUM	Water
> 
> 
> 
> I have 563 grid cells across my study area and each individual has 1-563
> cells associated for each year and each season the individual was monitored.
> Therefore my grid cells are repeated. I end up with 71,000 records and 925
> records have a Count value >0; which means 70,075 records have a Count value
> = 0. 
> 
> I wanted to run a zero inflated poisson model to determine mixed effects (of
> parameters) with individual as the random effect. But I have been advised
> two things:
> 
> 1. I cannot run a zero inflated poisson model because my data are too
> "extremely" inflated (i.e. 70,075 vs 925) and 
> 
> 2. I cannot run the model with each cell repeated for each individual. I am
> told the model doesn't recognize that Cell_ID #1 for individual "A" is the
> same Cell_ID #1 for individual "B".
> 
> Does anyone know if either or both of these points are true? I would
> appreciate any thoughts, advice, or suggestions. 
> 
> Thanks!
> 
> -Stephanie


Hi Stephanie,

Some comments:

1. You should think about or at least be open to a zero inflated negative binomial distribution rather than zero inflated poisson. 

2. You should at least review the vignette for the pscl CRAN package, which provides standard fixed effects models and related functions for count based data and importantly, some good conceptual content:

  http://cran.r-project.org/web/packages/pscl/vignettes/countreg.pdf

3. Given the repeated measures framework and correlation issues you likely have, you should subscribe to and re-post your query to the R-sig-mixed-models list:

  https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

which will avail you of experts in the field. 

4. There is also a draft FAQ for mixed models here:

  http://glmm.wikidot.com/faq

which I believe is maintained by Ben Bolker, who actively participates in the above list. Based upon the content there, I suspect that you will be pointed to the glmmADMB package which is on R-Forge (http://glmmadmb.r-forge.r-project.org/) and can handle zero inflated mixed effects models of at least some types.

5. If all else fails, just to plant a seed, you might want to consider a mixed effects logistic regression model with a binary response, since you appear to have a relatively small "event" incidence in your data. The above list will also be helpful in that setting and you would likely be pointed to the glmer() function in the lme4 package for that application, which provides for GLMs in a mixed effects framework.

Regards,

Marc Schwartz