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

[Gi-Mick Wu]

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