[R-sig-ME] Fwd: lme4, lme4a, and overdispersed distributions (again)
Jeffrey Evans
Jeffrey.Evans at dartmouth.edu
Mon Jun 28 22:44:41 CEST 2010
Hi Dave, I see that Ben Bolker et al's wiki page also references it.
I'm not able to get glmer to do this. I do something similar with my dataset
(dat$over = 1:nrow(dat)) and I get an error, not a warning.
> Xfit$over = 1:nrow(Xfit)
> m800 = glmer(cbind(gmdat$SdlFinal, gmdat$SdlMax-gmdat$SdlFinal)
~soilpc3+(1|gmdat$ID)+(1|over),data=Xfit, family="binomial")
Error in function (fr, FL, glmFit, start, nAGQ, verbose) :
Number of levels of a grouping factor for the random effects
must be less than the number of observations
What version are you using? I'm running version 33.
Cheers,
Jeff
John et al.--
Actually, looks like the current version of glmer *does* allow
observation level random-effects, though it throws you a little warning
(which seems entirely appropriate). (Thank you Doug!)
Using the data that we were recently discussing (and attached to one of
my previous posts "Data Redux"):
> drink.df$over <- 1:nrow(drink.df)
> drk.glmer <- glmer(drinks ~ weekday*gender + (1 | id) + (1 | over),
+ data = drink.df, family = poisson,
+ verbose = TRUE)
Number of levels of a grouping factor for the random effects
is *equal* to n, the number of observations
0: 96443.694: 1.63299 0.215642 -0.912787 -0.0135537 0.0244628
-0.0137854 0.504067 1.13637 1.06483 0.418800 0.366592 0.288067
0.354827 0.443268 0.392234 0.287877
[snip]
76: 73629.541: 4.35359 0.187209 -5.44079 -0.101647 -0.0249078
-0.0721097 0.513271 1.65032 1.51045 0.132999 0.435110 0.356431
0.382994 0.600458 1.26700 0.797529
> summary(drk.glmer)
Generalized linear mixed model fit by the Laplace approximation
Formula: drinks ~ weekday * gender + (1 | id) + (1 | over)
Data: drink.df
AIC BIC logLik deviance
73662 73805 -36815 73630
Random effects:
Groups Name Variance Std.Dev.
over (Intercept) 18.953746 4.35359
id (Intercept) 0.035047 0.18721
Number of obs: 56199, groups: over, 56199; id, 980
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.44079 0.15315 -35.53 < 2e-16 ***
weekdayMonday -0.10165 0.22164 -0.46 0.64651
weekdayTuesday -0.02491 0.21837 -0.11 0.90919
weekdayWednesday -0.07211 0.22089 -0.33 0.74408
weekdayThursday 0.51327 0.19953 2.57 0.01010 *
weekdayFriday 1.65032 0.17918 9.21 < 2e-16 ***
weekdaySaturday 1.51045 0.18023 8.38 < 2e-16 ***
genderM 0.13300 0.22493 0.59 0.55432
weekdayMonday:genderM 0.43511 0.31295 1.39 0.16442
weekdayTuesday:genderM 0.35643 0.31078 1.15 0.25142
weekdayWednesday:genderM 0.38299 0.31327 1.22 0.22150
weekdayThursday:genderM 0.60046 0.28439 2.11 0.03474 *
weekdayFriday:genderM 1.26700 0.25845 4.90 9.48e-07 ***
weekdaySaturday:genderM 0.79712 0.26107 3.05 0.00226 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
As an aside, it is interesting to see for this particular data how the
variance swings pretty wildly between the model without over-dispersion
to the current one:
> summary(drk.glmer)
Generalized linear mixed model fit by the Laplace approximation
Formula: drinks ~ weekday * gender + (1 | id)
Data: drink.df
AIC BIC logLik deviance
146572 146706 -73271 146542
Random effects:
Groups Name Variance Std.Dev.
id (Intercept) 0.92314 0.9608
Number of obs: 56199, groups: id, 980
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.23639 0.04863 -25.42 < 2e-16 ***
weekdayMonday -0.01035 0.03331 -0.31 0.756
weekdayTuesday 0.02583 0.03304 0.78 0.434
weekdayWednesday -0.01161 0.03341 -0.35 0.728
weekdayThursday 0.50049 0.02976 16.82 < 2e-16 ***
weekdayFriday 1.12677 0.02691 41.87 < 2e-16 ***
weekdaySaturday 1.05954 0.02709 39.11 < 2e-16 ***
genderM 0.30064 0.07099 4.24 2.28e-05 ***
weekdayMonday:genderM 0.36970 0.04359 8.48 < 2e-16 ***
weekdayTuesday:genderM 0.29552 0.04358 6.78 1.19e-11 ***
weekdayWednesday:genderM 0.36295 0.04378 8.29 < 2e-16 ***
weekdayThursday:genderM 0.45315 0.03913 11.58 < 2e-16 ***
weekdayFriday:genderM 0.40290 0.03587 11.23 < 2e-16 ***
weekdaySaturday:genderM 0.29764 0.03624 8.21 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
These data in all likelihood are probably best modeled by a two-part
model, with zero vs. non-zero and count model for non-zeroes. The
current version of MCMCglmm allows for zero-inflated models (where
zeroes are a mixture of a point mass and count distribution), and the
development version has hurdle formulations (with zero vs. non-zero, and
then truncated count distribution for non-zeroes).
cheers, Dave
John Maindonald wrote:
I think it more accurate to say that, in general, there may be
a class of distributions, and therefore a possible multiplicity
of likelihoods, not necessarily for distributions of exponential
form. This is a PhD thesis asking to be done, or maybe
someone has already done it.
Over-dispersed distributions, where it is entirely clear what the
distribution is, can be generated as GLM model + one random
effect per observation. We have discussed this before. This
seems to me the preferred way to go, if such a model seems to
fit the data. I've not checked the current state of play re fitting
such models in lme4 of lme4a; in the past some versions have
allowed such a model.
I like the simplicity of the one random effect per observation
approach, as against what can seem the convoluted theoretical
framework in which beta binomials live.
John Maindonald email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473 fax : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm
>
> On 25/06/2010, at 3:59 AM, Jeffrey Evans wrote:
>
>> Since I am definitely *not* a mathematician, I am straying in over
my head
>> here.
>>
>> I understand what you are saying - that there isn't a likelihood
function
>> for the quasi-binomial "distribution". And therefore, there is no-such
>> distribution.
>>
>> What do you think of the suggestion that a beta-binomial mixture
>> distribution could be used to model overdispersed binomial data?
>>
>> Would this be a techinically correct and logistically feasibile
solution?
>>
>> -jeff
>>
>> -----Original Message-----
>> From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf
Of Douglas
>> Bates
>> Sent: Thursday, June 24, 2010 1:25 PM
>> To: Jeffrey Evans
>> Cc: r-sig-mixed-models at r-project.org
>> Subject: Re: [R-sig-ME] lme4, lme4a, and overdispersed distributions
(again)
>>
>> On Thu, Jun 24, 2010 at 11:54 AM, Jeffrey Evans
>> <Jeffrey.Evans at dartmouth.edu> wrote:
>>> Like others, I have experienced trouble with estimation of the scale
>>> parameter using the quasi-distributions in lme4, which is necessary to
>>> calculate QAICc and rank overdispersed generalized linear mixed models.
>>
>>> I had several exchanges with Ben Bolker about this early last year
>>> after his TREE paper came out
>>> (http://www.cell.com/trends/ecology-evolution/abstract/S0169-5347%2809
>>> %29000 19-6), and I know it's been discussed on on this list. Has
>>> there been or is there any potential resolution to this forthcoming in
>>> future releases of
>>> lme4 or lme4a? I run into overdispersed binomial distributions
>>> frequently and have had to use SAS to deal with them. SAS appears to
>>> work, but it won't estimate the overdispersion parameter using laplace
>>> estimation (only PQL), As I understand it, these pseudo-Iikelihoods
>>> can't be used for model ranking. I don't know why SAS can't/won't, but
>>> lme4 will run these quasi-binomial and quasi-poisson distributions with
>> Laplace estimation.
>>
>>> Is there a workable way to use lme4 for modeling overdispersed
>>> binomial data?
>>
>> I have trouble discussing this because I come from a background as a
>> mathematician and am used to tracing derivations back to the original
>> definitions. So when I think of a likelihood (or, equivalently, a
>> deviance) to be optimized it only makes sense to me if there is a
>> probability distribution associated with the model. And for the
>> quasi-binomial and quasi-Poisson families, there isn't a probability
>> distribution. To me that means that discussing maximum likelihood
>> estimators for such models is nonsense. The models simply do not exist.
>> One can play tricks in the case of a generalized linear model to
estimate a
>> "quasi-parameter" that isn't part of the probability distribution
but it is
>> foolhardy to expect that the tricks will automatically carry over to a
>> generalized linear mixed model.
>>
>> I am not denying that data that are over-dispersed with respect to the
>> binomial or Poisson distributions can and do occur. But having data
like
>> this and a desire to model it doesn't make the quasi families real.
In his
>> signature Thierry Onkelinx quotes
>>
>> 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
>>
>> I could and do plan to incorporate the negative binomial family but,
without
>> a definition that I can understand of a quasi-binomial or quasi-Poisson
>> distribution and its associated probability function, I'm stuck. To
me it's
>> a "build bricks without straw" situation - you can't find maximum
likelihood
>> estimates for parameters that aren't part of the likelihood.
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
John Maindonald email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473 fax : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm
--
Dave Atkins, PhD
Research Associate Professor
Department of Psychiatry and Behavioral Science
University of Washington
datkins <at> u.washington.edu
Center for the Study of Health and Risk Behaviors (CSHRB)
1100 NE 45th Street, Suite 300
Seattle, WA 98105
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(Mon-Wed)
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Medically Vulnerable Populations (CHAMMP)
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