R help - Jan 2007 - Help with problem - multilevel model?

I have what is probably a very simple problem but I would be very
grateful to the list for any help or pointers to implement a solution in
R.

We have two types of measurements on the eye that we have collected in
62 patients at 5 fixed time points during a clinical visit over an
office day. We want to establish if there is an association between the
measurements. Obviously it would be wrong to generate a simple
scatterplot of all 62*5 observations and consider something like a
simple correlation coefficient. What I really need is to set up a
2-level model with measurements nested within patients and use, perhaps,
one variable as a response and the other as a predictor. I would also
like to add in time of day (probably as a categorical) to check this
isn't affecting things. I haven't used multi-level modelling in R and
wonder how I can simply go about fitting this model and looking at the
significance of the estimates in R. I also have a plot in my mind - 62
little regression lines (n=5) and think that this might be
informative.....

Any help or pointers will be gratefully received - Many Thanks.

Dr. David Crabb
Department of Optometry and Visual Science,
City University, Northampton Square, London EC1V OHB
Tel: 44 207 040 0191   d.crabb at city.ac.uk
http://www.city.ac.uk/optometry/about/staff/crabb.html

This should get you started


tmp <- data.frame(y1=rnorm(62*5),
                  y2=rnorm(62*5),
                  time=rep(1:5, 62),
                  id=factor(rep(1:62, each=5))
                  )

xyplot(y1 ~ y2 | id, data=tmp, group=time, pch=as.character(1:5))

tmp.aov <- aov(y1 ~ y2*factor(time) + Error(id), data=tmp)
summary(tmp.aov)

Aov is not the right function for this problem. Lmer is designed for
multilevel modeling. There are a lot of resources, but start with the
following vignette

Library(lme4)
vignette("MlmRevSoft")

And then turn to Pinhiero and Bates
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
> Richard M. Heiberger
> Sent: Thursday, January 18, 2007 10:22 AM
> To: Crabb, David; r-help at stat.math.ethz.ch
> Subject: Re: [R] Help with problem - multilevel model?
> 
> This should get you started
> 
> 
> tmp <- data.frame(y1=rnorm(62*5),
>                   y2=rnorm(62*5),
>                   time=rep(1:5, 62),
>                   id=factor(rep(1:62, each=5))
>                   )
> 
> xyplot(y1 ~ y2 | id, data=tmp, group=time, pch=as.character(1:5))
> 
> tmp.aov <- aov(y1 ~ y2*factor(time) + Error(id), data=tmp)
> summary(tmp.aov)
> 
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