[R-sig-ME] Help understanding residual variance

[Ista Zahn]

Thank you Greg, that helps.

-Ista

On Tue, Mar 27, 2012 at 11:32 AM, Greg Snow <538280 at gmail.com> wrote:
>
> Yes, each person has their own slope and intercept estimated, however
> the slope and intercept are not determined solely by the 2 data points
> for that person, but also are affected by the slope and intercept
> estimates across all subjects (this is why lmer gives value beyond
> lmList).
>
> You can see this if you refit using the nlme package (only because it
> has the augPred function which has not been implemented in lme4 yet):
>
> library(nlme)
> m2 <- lme( Reaction ~ Days, data=tmp, random=~Days|Subject)
> plot(augPred(m2, ~Days, level=c(0,1)))
>
> comparing the m2 model to your m1 gives the same fixed effects, but
> slightly different random effects (I probably did not do something
> that was needed to make the models exactly the same) but is probably
> close enough.
>
> Look at the plot and you will see the fixed effects line, the line for
> each subject that includes the random effects, and the data.  The line
> for the individual subjects are pulled slightly towards the fixed
> effects line and so does not hit the 2 points exactly.  This shows how
> the estimate of each individuals values are influenced by the overall
> fit.
>
>
> On Mon, Mar 26, 2012 at 8:18 PM, Ista Zahn <istazahn at gmail.com> wrote:
> > Hi all,
> >
> > I'm trying to understand what the residual variance in this model:
> >
> > tmp <- subset(sleepstudy, Days == 1 | Days == 9)
> > m1 <- lmer(Reaction ~ 1 + Days + (1 + Days | Subject), data = tmp)
> > tmp$fitted1 <- fitted(m1)
> >
> > represents. The way I read this specification, an intercept and a
> > slope is estimated for each subject. Since each subject only has two
> > measurements, I would expect the Reaction scores to be completely
> > accounted for by the slopes and intercepts. Yet they are not: the
> > Residual variance estimate is 440.278.
> >
> > This is probably a stupid question, but I hope you will be kind enough
> > to humor me.
> >
> > Best,
> > Ista
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>
>
> --
> Gregory (Greg) L. Snow Ph.D.
> 538280 at gmail.com