Help understanding residual variance
Hello again, Sorry for bringing this up again. The thing is that a statistician consulting with my research group insists that you cannot have both random intercepts and random slopes when there are only two observations per group. Clearly I can fit such a model using lmer(), but this only serves to convince my local statistician that "R is doing something strange". I suspect that this is a hopelessly vague question, but is R doing something strange? Or is my statistician incorrect in claiming that you can't fit both random intercepts and random slopes with only two observations per group? Again, I realize this is not a great question, but I would really appreciate any thoughts on the matter. Best, Ista
On Tue, Mar 27, 2012 at 2:55 PM, Ista Zahn <istazahn at gmail.com> wrote:
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
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-- Gregory (Greg) L. Snow Ph.D. 538280 at gmail.com