[R] glmmPQL and anova

[Maarten Speekenbrink]

Dear R-users,

I have conducted an experiment with a 2*2*2 factorial within-subjects design. All factors are binary and the dependent measure is a frequency of successes between 0 and 4. Treating this as a normally distributed variable, I would perform a repeated-measures ANOVA as follows:

> aov(y ~ A*B*C + Error(subj/(A+B+C)))

but since the distribution of the dependent measure is clearly nonnormal, I would like to fit an analoguous model which is appropriate and I believe this would be a GLMM with a logit link and a random intercept for subjects. I have fitted this model using 'glmmPQL' function in MASS as:

> glmmPQL(cbind(y,4-y) ~ A*B*C, random = ~ 1|subj, family=binomial(),data)

which seemed to do the trick. But I would like to present the results in an ANOVA-type table so that they are easiliy interpretable for the readers. I know the anova(glm, test="Chisq") function for fixed-effect GLM gives a ANOVA-type analysis in terms of the sequential Chi-Square difference tests, but since the glmmPQL function returns an object of the class lme, I wonder if the results of an anova(glmPQL) are appropriate. From an earlier posting I gathered that anova and AIC are inappropriate for model comparisons when the models are estimated by glmmPQL, since the estimation is not maximum likelihood, but does this hold for the anova applied to a single model?

Kind regards,

Maarten Speekenbrink
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 drs. M. Speekenbrink
 Psychological Methodology
 Department of Psychology, Faculty of Social and Behavioral Sciences
 address: Roeterstraat 15, 1018 WB Amsterdam, Netherlands
 tel: +31 20 525 6876 / +31 20 525 6870
 fax: +31 20 639 0026
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