[R-sig-ME] Linear mixed model query

[Etn bot]

Many thanks for your response Ben, it is greatly appreciated


Kind regards

Etn

On 25 September 2015 at 20:47, Ben Bolker <bbolker at gmail.com> wrote:

> On Thu, Sep 24, 2015 at 10:06 AM, Etn bot <etnbot1 at gmail.com> wrote:
> > Hi all,
> >
> > My study looks at allergy levels of skin patches from patients and
> readings
> > (repeated 5 times) are measured over 4 time points
> >
> > I need to determine if the allergy level for skin patch changes over time
> > (e.g. if allergy level from skin patch 1 for patient 1 at time 0 is
> > different from allergy level for skin patch 1 for patient 1 at time 1
> etc.)
> > I do not want to see the difference between skin patch 1 and skin patch
> > 2....
> >
> > using package lmer:
> > model<-lmer(allergy_level ~ time +(time|patient/patch))
> >
> > Results from this model indicate that time is not significant - the
> average
> > patient allergy level for individual skin patches does not change over
> > time:
> >
> > Random effects:
> >
> >  Groups   Name        Variance Std.Dev. Corr
> >
> >  ID:patch (Intercept) 17.4109  4.1726
> >
> >           time1        2.7109  1.6465   -0.30
> >
> >           time2        3.0082  1.7344   -0.26  0.60
> >
> >           time3        5.7643  2.4009   -0.35  0.15  0.54
> >
> >  patch    (Intercept) 19.1576  4.3769
> >
> >           time1        0.2103  0.4586   -0.56
> >
> >           time2        0.4372  0.6612   -0.94  0.48
> >
> >           time3        0.5895  0.7678   -0.48  0.96  0.49
> >
> >  Residual              4.9467  2.2241
> >
> > Number of obs: 2956, groups:  ID:patch, 149; patch, 16
> >
> >
> >
> > Fixed effects:
> >
> >             Estimate Std. Error t value
> >
> > (Intercept)  6.44763    1.15028   5.605
> >
> > time1       -0.01907    0.21237  -0.090
> >
> > time2       -0.03172    0.24759  -0.128
> >
> > time3       -0.01124    0.29940  -0.038
> >
> >
>    I was going to ask if you wanted to treat time as linear, but there's
> not much evidence that it will help you here.
> >
> >
> >
> > model1: Force ~ 1 + (1 + time | patch/ID)
> >
> > model2: Force ~ time + (1 + time | patch/ID)
> >
> >          Df   AIC   BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
> >
> > model11 22 14281 14413 -7118.5    14237
> >
> > model12 25 14287 14437 -7118.4    14237 0.0208      3     0.9992
> >
> > I have extracted the random coefficients from model 1:
> >
> > ranef(model1)
> >
> > $`ID:patch`
> >
> >       (Intercept)       time1        time2        time3
> >
> > 1:11    5.9845070  0.34088535  0.431998708  1.590906238
> >
> > 1:12    5.1236456 -0.03178611 -0.149784278 -0.116150278
> >
> > 1:13    6.3746877 -0.76853294 -0.550037715  0.842518786
> >    :
> >    :
> > However, I need to be able to tell if there is a significant difference
> for
> > individual patches for individual patients over time
> >
> > e.g.
> > If I run individual linear regression on patient 1 for skin patch 1,
> > results show that that time is significant:
> >
> > Coefficients:
> >
> >             Estimate Std. Error t value Pr(>|t|)
> >
> > (Intercept)  18.0800     0.6523  27.717 5.95e-15 ***
> >
> > time1         0.3600     0.9225   0.390 0.701502
> >
> > time2         1.2400     0.9225   1.344 0.197641
> >
> > time3        -4.3400     0.9225  -4.705 0.000239 ***
> >
> > ---
> >
> > Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> >
> >
> >
> > Residual standard error: 1.459 on 16 degrees of freedom
> >
> > Multiple R-squared:  0.7323,    Adjusted R-squared:  0.6821
> >
> > F-statistic: 14.59 on 3 and 16 DF,  p-value: 7.679e-05
> >
> >
> > If I run individual regression models for each skin patch for each
> patient,
> > this will result in a large number of models as I have There are 16 skin
> > patches per patient. (10 patients in total) 5 readings are taken at each
> of
> > the 4 time points.
> >
> > I thought linear mixed models would be an appropriate method to answer my
> > question (I need to be able to tell if there is a significant difference
> > for individual patches for individual patients over time).
> >
>
>   When you adopt a random-effects formulation, you forego the ability
> to perform significance tests on individual levels -- that's the price you
> pay for the benefits of doing shrinkage estimation.  If you need
> significance
> tests on individual patch/patient combinations, you're going to be
> stuck with 160 significance tests (you should probably consider some
> kind of multiple-comparisons correction ...)
>
>  Ben Bolker
>

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