[R-sig-ME] mean and variance of random effects in glmer
Ken Kelley
kkelley at nd.edu
Tue Jul 24 20:38:20 CEST 2012
Hi Thierry,
Thanks for your thoughts on this. I hadn't considered quasi-separation, but I don't think that is it. Actually, the issue is that I slipped into thinking that the random effects were the conditional means (like in a linear mixed effects model). Rather, they are the conditional modes. Thus, the mean of the random effects need not be zero as I initially expected (and as would be the case in a linear mixed effects model).
But, I still expected the variance of the random effects to match the output (it is 18.9 in the output yet 7.8 when I calculate it on the random effects directly).
Best wishes,
Ken
On Jul 24, 2012, at 5:23 AM, "ONKELINX, Thierry" <Thierry.ONKELINX at inbo.be> wrote:
> Dear Ken,
>
> Very large variance for the random effect in a binomial glmer is an indication for (quasi-)complete separation. Here is some info on that issue: http://www.ats.ucla.edu/stat/mult_pkg/faq/general/complete_separation_logit_models.htm
>
> If the values of Problem and Across are constant within each level of PID, I would aggregate the data (sum per PID) and then use a simple glm()
>
> Best regards,
>
> Thierry
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest,
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
> + 32 2 525 02 51
> + 32 54 43 61 85
> Thierry.Onkelinx at inbo.be
> www.inbo.be
>
> To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
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> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] Namens Ken Kelley
> Verzonden: dinsdag 24 juli 2012 8:29
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: [R-sig-ME] mean and variance of random effects in glmer
>
> Hi everyone,
>
> I'm fitting a straightforward glmer model with the family=binomial. I expected the mean of the random effect for the intercept to be near zero, but that isn't the case, as the mean is .91:
>
>> (model.3 <- glmer(TA ~ 1 + Problem + Across + (1|PID), data=Data.Timed, family = binomial, nAGQ=100))
> Generalized linear mixed model fit by the adaptive Gaussian Hermite approximation
> Formula: TA ~ 1 + Problem + Across + (1 | PID)
> Data: Data.Timed
> AIC BIC logLik deviance
> 158.8 172.9 -75.38 150.8
> Random effects:
> Groups Name Variance Std.Dev.
> PID (Intercept) 18.869 4.3439
> Number of obs: 256, groups: PID, 64
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.1328 0.7304 -1.551 0.1209
> Problem -0.5864 0.2449 -2.394 0.0167 *
> Across -1.3768 0.4280 -3.217 0.0013 **
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Correlation of Fixed Effects:
> (Intr) Problm
> Problem -0.390
> Across -0.208 -0.150
>
> That is, I'm doing a mixed effects logistic regression. The PID is the participant ID; there are 4 Problems (essentially timepoints: 0, 1, 2, 3) and Across is a time-varying covariate (0, 1, 2, or 3).
>
> The mean of the random effects is:
>> colMeans(ranef(model.3)$PID[])
> (Intercept)
> 0.9137307
>
> Additionally, the variance of the random effect is in the model output as 18.869, yet when I calculate the variance of the random effects directly, I get a much smaller value:
>> var(ranef(model.3)$PID[])
> (Intercept)
> (Intercept) 7.806402
>
> Should I be surprised by either of the issues I note above? My concern is that I was planning on plotting the model implied curves using the fixed effects (so that the curves would represent an individual specific trajectory for a participant with a random effect of 0). Yet, there are no individuals with a random effect of zero and the mean is not zero. Thus, such a plot doesn't seem as useful as I initially thought it would.
>
> Thanks for any thoughts on this,
> Ken
>
>
>
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