[R-sig-ME] Advise on mixed effect model for a longitudinal study (with lme4)
wphantomfr
wphantomfr at gmail.com
Thu Oct 8 16:12:38 CEST 2015
Dear Thierry,
First thanks a lot for taking time to answer me.
Thierry Onkelinx wrote:
> Dear anonymous.
oups.. I forgot to Sign
>
> Your random effects seem a bit to complicated for your data. A random
> slope with 6 observations per subject is pushing the limits. A second
> degree polynomial on 6 observations is nonsense. I can understand that
> is does make sense on a conceptual level, but you just don't have enough
> data to get sensible estimates on such a complex model.
>
> My advice would be to restrict the random effect to just a random
> intercept. The benefit is that you gain 5 parameters and their
> associated degrees of freedom. Note that a second order polynomial on
> the fixed effect might be feasible.
I think I understand the problem but did not realize I was pushing the
limits doing this because (1) it was making sense to use random slopes
when looking at the data and (2) I was probably too much focused on the
results of model comparisons that indicated a better fit for this
complex model.
But is there a way to know that we are pushing too much the limits ?
Would only the random intercept + linear slope be acceptable (however
the linear slope is probably optimal with our design)
>
> You probably want to translate your hypotheses in a set of linear
> combination of model parameters. Then you can test those hypotheses.
> Have a look at the examples in the glht() function fom the mulcomp package.
Well that's exactly that... I just didn't realise that glht could work
with lme models
>
> PS Please don't post in HTML. It mangles up the output and code.
sorry. I think I have now disabled the default HTML mode.
Thank you very much for your help !
Sylvain CLEMENT
PSITEC (EA 4072) laboratory
"Neuropsychologie : Audition, Cognition, Action (NACA)" team
University of Lille, France.
>
> Best regards,
>
> 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
>
> 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
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of
> data. ~ John Tukey
>
> 2015-10-08 10:59 GMT+02:00 wphantomfr <wphantomfr at gmail.com
> <mailto:wphantomfr at gmail.com>>:
>
> Dear list members,
>
> I currently trying to apply mixed effects models to a longitudinal
> studies with a treatment period.
>
> The study is :
> Several evaluation of a participants characteristic (let's call it DV)
> at different times (in week) : 0 (1 evaluaition), 1 , 3, 6, 8 10.
>
> We have 3 different groups of participants (randomized controlled study)
> : a control group without treatment and groupA and groupB which received
> a different treatment.
>
> The treatment is applied to the groupA & B during weeks 2-5 therefore :
> - evaluations at w0 and w1 are "baseline measures" (pre-treatment)
> - evaluation at w3 is during treatment
> - evaluation at w6 is post treatment
> - evaluation at w8 & w10 are follow-up evaluation.
>
>
>
> After reading a lot on mixed effects model I arrived to the following
> model (using lme4 package):
>
> best_model<-lmer(DV ~ (time+I(time^2))*GROUP
> +(1+(time+I(time^2))|SUBJECT),data=brut)
>
> It includes a quadratic effect of time (continuous variable) and both
> intercept and "slopes" (not a good word for the quadratic par) of the
> effects of time (both linear and quadratic) are estimated for the random
> effects of SUBJECT.
>
> This model seems to be the best compared to models including only parts
> of these terms (model comparison with anova ). The summary report of the
> model is pasted at the end of this message
>
>
> My hypothesis are :
> - that I should see a superior effect of time in group A & B (if
> the treatment increases DV, I should have a positive coeficient for time
> and a negative coeficient for time^2)
> - that the effect of time may be superior in group B compared to
> group A
> - I would also like to see if one of the treatment have a more
> long-term effect (sustained effect in the foloup evaluations)
>
> I'm not sure how to test/answer my questions from my model.
>
>
>
>
> My guesses :
> - the fact that GROUPA et GROUPB have low t-values is a sign that my
> groups are quite similar at the begining of the study
> - The coeficient of time:GROUP(A & B) and I(time^2):group(A&B) are in
> line with my hypothesis
> - I don't know how, in this context, I can answer to the question of
> long-term effects...
>
>
> My questions :
>
> Am I totally wrong ?
>
> How to best assess my hypothesis ?
>
> Any more advises ?
>
>
> Thanks in advance
>
>
>
>
> Here is the model report :
>
>
> summary(bestM)
> Linear mixed model fit by REML
> t-tests use Satterthwaite approximations to degrees of freedom
> ['lmerMod']
> Formula: DV ~ (time + I(time^2)) * GROUP + (1 + (time + I(time^2))
> | SUBJECT)
> Data: brut
>
> REML criterion at convergence: -458.9
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -3.1714 -0.3972 0.0660 0.4385 2.7059
>
> Random effects:
> Groups Name Variance Std.Dev. Corr
> SUBJECT (Intercept) 6.201e-02 0.24902
> time 2.042e-03 0.04519 -0.45
> I(time^2) 1.162e-05 0.00341 0.41 -0.95
> Residual 1.314e-02 0.11462
> Number of obs: 710, groups: CODE, 117
>
> Fixed effects:
> Estimate Std. Error df t value
> Pr(>|t|)
> (Intercept) 1.858e-01 4.557e-02 1.140e+02 4.078
> 8.44e-05 ***
> time 1.960e-03 1.159e-02 1.138e+02 0.169 0.86599
> I(time^2) 2.149e-04 1.032e-03 1.137e+02 0.208 0.83547
> GROUPA -2.006e-02 6.198e-02 1.140e+02 -0.324
> 0.74681
> GROUPB -2.898e-02 6.094e-02 1.138e+02 -0.476
> 0.63531
> time:GROUPA 3.837e-02 1.576e-02 1.138e+02 2.435
> 0.01645 *
> time:GROUPB 4.212e-02 1.546e-02 1.120e+02 2.724
> 0.00748 **
> I(time^2):GROUPA -2.749e-03 1.404e-03 1.137e+02 -1.957
> 0.05277 .
> I(time^2):GROUPB -3.222e-03 1.377e-03 1.113e+02 -2.340
> 0.02108 *
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
> (Intr) time I(t^2) GROUPA GROUPB t:GROUPA t:GROUPB
> I(^2):GROUPA
> time -0.467
> I(time^2) 0.379 -0.951
> GROUPA -0.735 0.343 -0.279
> GROUPB -0.748 0.349 -0.283 0.550
> t:GROUPA 0.343 -0.735 0.699 -0.467 -0.257
> t:GROUPB 0.350 -0.749 0.712 -0.257 -0.467 0.551
> I(^2):GROUPA -0.279 0.699 -0.735 0.379 0.208 -0.951 -0.524
> I(^2):GROUPB -0.284 0.713 -0.750 0.209 0.379 -0.524 -0.951 0.551
>
>
> [[alternative HTML version deleted]]
>
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