R help - Jan 2003 - glmmPQL and anova

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
--------------------------------------------------------------------
 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
--------------------------------------------------------------------

Yes.

On Tue, 14 Jan 2003, Maarten Speekenbrink wrote:
> 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
> --------------------------------------------------------------------
>  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
> --------------------------------------------------------------------
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595