R help - Aug 2006 - Linear Trend in Residiuals From lme

I'm fitting a mixed effects model:

fit.1 <- lme(y~x,random=~1|id,data=df)

There are two different observations for each id for both x and y. When
I use plot(fit.1), there is a strong increasing linear trend in the
residuals versus the fitted values (with no outliers). This also happens
if I use random=~x|id. Am I specifying something incorrectly?

Rick B.

On 8/9/06, Rick Bilonick <rab45+ at pitt.edu>
wrote:
> I'm fitting a mixed effects model:
>
> fit.1 <- lme(y~x,random=~1|id,data=df)
>
> There are two different observations for each id for both x and y. When
> I use plot(fit.1), there is a strong increasing linear trend in the
> residuals versus the fitted values (with no outliers). This also happens
> if I use random=~x|id. Am I specifying something incorrectly?
Could you provide a reproducible example please?

I suspect that the problem comes from having only two observations per
level of id.  When you have very few observations per group the roles
of the random effect and the per-observation noise term in explaining
the variation become confounded.  However, I can't check if this is
the case without looking at some data and model fits.

As an extreme example of this sort of thing, consider

fit <- lme(y ~ 1, random = ~ 1 | group)

where there is exactly one observation per group, so that it is not possible to
get separate estimates of group and residual variances.  Despite this, lme
often (always?) provides a solution consistent with the data. Because of the
singularity, the plot of residuals against fitted values for this solution
shows a straight line.  This is easily recognized as an aberration, but I can
imagine configurations of data (e.g. with most groups having just one
observation and a few with two or more) where the residual vs fitted value plot
might show an apparent trend.



On Wed, Aug 09, 2006 at 03:43:12PM -0400, Rick Bilonick
wrote:
> I'm fitting a mixed effects model:
> 
> fit.1 <- lme(y~x,random=~1|id,data=df)
> 
> There are two different observations for each id for both x and y. When
> I use plot(fit.1), there is a strong increasing linear trend in the
> residuals versus the fitted values (with no outliers). This also happens
> if I use random=~x|id. Am I specifying something incorrectly?
> 
> Rick B.
> 
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