[R-sig-ME] Advise on mixed effect model for a longitudinal study (with lme4)
Thierry Onkelinx
thierry.onkelinx at inbo.be
Thu Oct 8 13:57:30 CEST 2015
Dear anonymous.
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.
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.
PS Please don't post in HTML. It mangles up the output and code.
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 op 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
>
>
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