[R] lmer and a response that is a proportion

[John Fox]

Dear Cameron,

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Cameron Gillies
> Sent: Sunday, December 03, 2006 1:58 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] lmer and a response that is a proportion
> 
> Greetings all,
> 
> I am using lmer (lme4 package) to analyze data where the 
> response is a proportion (0 to 1).  It appears to work, but I 
> am wondering if the analysis is treating the response 
> appropriately - i.e. can lmer do this?
>

As far as I know, you can specify the response as a proportion, in which
case the binomial counts would be given via the weights argument -- at least
that's how it's done in glm(). An alternative that should be equivalent is
to specify a two-column matrix with counts of "successes" and "failures" as
the response. Simply giving the proportion of successes without the counts
wouldn't be appropriate.
 
> I have used both family=binomial and quasibinomial - is one 
> more appropriate when the response is a proportion?  The 
> coefficient estimates are identical, but the standard errors 
> are larger with family=binomial.
>

The difference is that in the binomial family the dispersion is fixed to 1,
while in the quasibinomial family it is estimated as a free parameter. If
the standard errors are larger with family=binomial, then that suggests that
the data are underdispersed (relative to the binomial); if the difference is
substantial -- the factor is just the square root of the estimated
dispersion -- then the binomial model is probably not appropriate for the
data.

I hope this helps,
 John
 
> Thanks very much for any insight you may have!
> Cam
> 
> 
> Cam Gillies
> PhD Candidate
> Biological Sciences
> University of Alberta
> 
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