[R-sig-ME] Correct dispersion parameter for glmmML?

[Ken Beath]

In your model fitting you have the intercept estimate large and with  
large standard error and similarly for Ordr and maybe Exposure. This  
is usually an indication of a problem with the fitting of binomial  
data, probably separation due to overfitting. I would start with a  
simple model and try and work out which terms are causing problems.

I prefer not to think about overdispersed GLMM, they seem a bit odd  
statistically, maybe a GEE based approach is better.

Ken

On 25/03/2009, at 7:07 AM, Gi-Mick Wu wrote:

> Dear mixed model users, (my first post, after reading the archives a  
> lot)
>
> This post is about mixed models, but not lmer or lme4; please let me  
> know if it is inappropriate. (I have searched the archives for hours  
> without finding an answer to my question. I have also searched and  
> posted in "R-sig-eco" without results).
> Thank you in advance for reading!
>
> I’m fitting a generalized linear mixed model to binary data using  
> glmmML (version 0.81-4), but am unsure of how to obtain the correct  
> dispersion parameter. (I have also just updated R to version 2.8.1)
>
> For a glm model, I read that it should be the SS Pearson's  
> residuals / df, rather than the default residuals (deviance). In my  
> case:
>
> # GLM
> # using Pearson's residuals:
>> sum(residuals(modl.glm,type="pearson")^2)/modl.glm$df.residual
> [1] 1.062947
> # using deviance
>> modl.glm$deviance/modl.glm$df.residual
> [1] 1.409863
>
> For glmmML however, I cannot obtain the pearson residuals, but only  
> the deviance and null deviance (same as deviance for glm):
>
> # GLMM
> # using Pearson's residuals
>> residuals(modl.glmmML)
> NULL
> # using deviance
>> modl.glmmML$deviance/modl.glmmML$df.residual
> [1] 1.413364
> # using null deviance
>> modl.glmmML$cluster.null.deviance/modl.glmmML$cluster.null.df
> [1] 1.409863
>
> I am confused as to which (if any) of the dispersion parameter is  
> valid for the glmm model. Any one have an idea?
>
> Thanks in advance for reading and hopefully for some much needed  
> answers or pointers.
> Mick
> PS In case it is relevant or for curiosity's sake, here's the  
> experimental design:
>
> The experiment consists in testing the effect of experience on odour  
> preferences of parasitoid wasps. Parasitoids lay eggs in host  
> insects, which will be devoured from the inside until they die; like  
> the movie Alien :-)
>
> Wasps were exposed to two different odours, with or without the  
> presence of hosts (call them rewarded / unrewarded odour). Their  
> odour preference was then tested in a Y-tube olfactometer 5 times  
> after exposure (2h, 6h, 26h, 50h, 98h). 36 individuals were exposed  
> to each odour either 1,2,3, or 4 times (9 individuals/treatment  
> level). Odours were presented in alternation with half the wasps  
> starting with the rewarded odour.
> (Total number of binary choices = 180). I set Time and NbExposure as  
> fixed effects because I'm really interested in their effect and wasp  
> ID as random. I also added body size, which seem to play a role on  
> the effect of experience in honeybees, but it is secondary, so it  
> could be removed (to avoid overfitting).
>
> # R code for fitting the glmm
> form <- cbind(RewardOdour, UnrewardOdour) ~ (Time + NbExposure +  
> Ordr + BodySize)^2
> # interaction terms limited to second order for parsimony
> modl.glmmML <- glmmML(form, family=binomial,  
> data=clean.dat,cluster=clean.dat[,"ID"],
> 			prior="gaussian", method="ghq", n.points=8)           # same  
> results with n.points = 20
>
>> modl.glmmML
>
> Call:  glmmML(formula = form, family = binomial, data = clean.dat,  
> cluster = clean.dat[, "ID"], prior = "gaussian", method = "ghq",  
> n.points = 8)
>
>                                     coef            se(coef)       
> z           Pr(>|z|)
> (Intercept)             -7.539e+00  7.5906651  -0.99324   0.3210
> Time                        -6.303e-03   0.0648177  -0.09724   0.9230
> Exposure                 2.843e+00  2.3465958   1.21139   0.2260
> Ordr                         4.366e+00  5.1119166   0.85401   0.3930
> BodySize                  1.324e-02   0.0126869   1.04333   0.2970
> Time:Exposure         1.295e-03   0.0042982   0.30123   0.7630
> Time:Ordr                 2.042e-02   0.0093118   2.19259   0.0283
> Time:BodySize         -2.554e-06  0.0001093  -0.02337   0.9810
> Exposure:Ordr        -2.333e-01  0.3489015  -0.66859   0.5040
> Exposure:BodySize  -4.833e-03   0.0037688  -1.28235   0.2000
> Ordr:BodySize          -7.487e-03   0.0086466  -0.86585   0.3870
>
> Scale parameter in mixing distribution:  0.484 gaussian
> Std. Error:                                       0.3204
>
> Residual deviance: 237.4 on 168 degrees of freedom      AIC: 261.4
>
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