Correlated Count Data

Message: 1
Date: Mon, 9 Jan 2012 09:07:21 +0000
From: "ONKELINX, Thierry" <Thierry.ONKELINX at inbo.be>
To: Lee Davis <m.lee.davis at gmail.com>,
       "r-sig-mixed-models at r-project.org"      <
r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Correlated count data technique advice
Message-ID:
       <AA818EAD2576BC488B4F623941DA742757324440 at inbomail.inbo.be>
Content-Type: text/plain; charset="us-ascii"

Dear Lee,

A large numbers of zero do not imply zero-inflation. E.g.

mean(rpois(10000, 0.01) == 0)

[1] 0.9902
This simulation has 99% zero's and is not zero-inflated.

Since you have a timeserie at only one location and one measurement 
per year there is no point in using a mixed model.

Wouldn't it be more relevant to look directly at the temperature than 
using a derived variable?

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature 
and Forest team Biometrie & Kwaliteitszorg / team Biometrics & Quality 
Assurance Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no 
more than asking him to perform a post-mortem examination: he may be 
able to say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does 
not ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org [mailto:
r-sig-mixed-models-bounces at r-project.org] Namens Lee Davis
Verzonden: vrijdag 6 januari 2012 19:54
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] Correlated count data technique advice

Please excuse me for having posted a similar question on ecolog, but 
thus far I have received few useful answers there.

I am looking for some advice concerning techniques in R that are 
appropriate for correlated count data.

Specifically, I have some "freezing days" data, which is a count of 
the number of days each spring that were below freezing. The counts 
were taken at the same location over a period of years. The data set 
is highly zero inflated and over-dispersed; glm with a quasipoisson 
error structure would seem to be appropriate, except that there is a 
high degree of correlation at lags of 1 making something like a corAR1 
structure appropriate. My difficulty is that glm() does not take an argument for correlation.

I could use  lmer() to fit a model like:

freezing days~years+(1|years), family=quasipoisson, correlation=corAR1

but lmer (and glmer) don't seem to be operating on quasi families 
anymore; I've found plenty of old posts here where lmer seems to have 
accepted quasi families in the past, but I get an error message that 
indicates lmer does not in fact accept quasi families.

I should note that I have run the following model:

 freeze.glmmPQL3<-glmmPQL(num.
freeze.days~years, random= ~1|years,
      family=quasipoisson,correlation=corAR1())

My gut says this is not the correct approach and I am unconvinced by 
the tiny p values that have been returned, especially as specification 
of poisson vs quasipoisson and the specification of corAR1() seem to 
make no difference to parameter estimation or p vals for said pars--it 
would seem that the random term for varying intercept by year is 
dominant. Maybe this is OK, but my above glm models return 
non-significant results and I expected handling the correlation to 
increase my p vals rather than decrease them. Perhaps an incorrect assumption.

Therefore I need some alternative to look at trends in this data over 
time that allows for quasipoisson error and something along the lines 
of a
corAR1() structure (or a mixed model that handles temporal 
pseudo-replication, but I am hesitant here).

Thank you in advance,
Lee