[R-sig-ME] strange model fit- help
marKo
mtonc|c @end|ng |rom ||r|@hr
Thu Mar 26 16:08:15 CET 2020
Thank a lot for the hints.
Rescaling into minutes helped a little. I would like to retain both the
raw polynomial terms, both the non-centered time (for ease of
readability). The model was written explicitly (not poly(time, 2,
raw=TRUE) for the same reasons.
The random part is quite complex but i will retain it as it is, because
of the almost perfect fit.
Thanks,
Marko
On 15. 03. 2020. 13:14, Thierry Onkelinx wrote:
> Dear Marko,
>
> Keep in mind that squating time in seconds lead to large numbers (489 ^
> 2 = 239121). This forces the parameters estimates to be small. You can
> solve this either by using orthogonal polynomial (poly(t, 2)) or by
> rescaling t (e.g. in minutes rather than seconds: 489 s = 8.15 min, 8.15
> ^ 2 = 66.4225) If you go for rescaling, then create 2 variables: t_min
> and t_min2 (= t_min ^ 2). That will make your formula more reable.
>
> It looks like you coded stim as an ordered factor. That not required
> since you have only two levels. Use a default factor with before as
> reference.
>
> The problem with the strong correlations between t and t^2 random
> effects is that they are highly correlated themselves. cor(0:489,
> (0:489) ^ 2) = 0.986 Note that is isn't solved by rescaling. Only
> centering works .eg centering at 4 minutes yields cor(0:489 - 4 * 60 /
> 60, (0:489 - 4 * 60) ^ 2) = 0.071 Orthogonal polynomials have the
> benefit that they are uncorrelated by definition. cor(poly(0:489, 2))
>
> Bottomline: always scale and center polynomials. I prefer to scale and
> center to revelant values, e.g. scale to a different unit and center to
> an important point near the middle of the domain. That keeps your
> parameters interpretable without the need to recalculate them (as you
> would when scaling by the standard deviation and center to the mean).
>
> Best regards,
>
> Thierry
>
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
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> AND FOREST
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>
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>
> Op za 14 mrt. 2020 om 17:10 schreef marKo via R-sig-mixed-models
> <r-sig-mixed-models using r-project.org
> <mailto:r-sig-mixed-models using r-project.org>>:
>
> Hi.
>
> I have fitted a relatively complicated model to electrodermal data (a
> simple resting and stimulus situation). The data summary follows.
>
> > summary(data)
> id sc t stim
> g1_1 : 49 Min. :26798 Min. : 1.0 before :3201
> g1_12 : 49 1st Qu.:32299 1st Qu.:123.0 after :1543
> g1_13 : 49 Median :32486 Median :245.0
> g1_14 : 49 Mean :32253 Mean :244.9
> g1_15 : 49 3rd Qu.:32587 3rd Qu.:367.0
> g1_2 : 49 Max. :32761 Max. :489.0
> (Other):4450
>
> id (person), and stim are factors, t is time (in s) and sc is skin
> conductance level. Sc distribution is quite negatively asymmetrical at
> the dataset level, although not that bad at the id level. As the
> stimulus occur at a specified time, those two variables are correlated
> (0.81).
>
> The model follows.
>
> m1<-lmer(sc~1+t+I(t^2)+stim+stim:t+stim:I(t^2)+(1+t+I(t^2)+stim+stim:t+stim:I(t^2)|id),
>
> data=data)
>
> Here goes the summary.
>
> > summary(m1)
> Linear mixed model fit by maximum likelihood ['lmerMod']
> Formula: sc ~ 1 + t + I(t^2) + stim + stim:t + stim:I(t^2) + (1 + t +
> I(t^2) + stim + stim:t + stim:I(t^2) | id)
> Data: data
>
> AIC BIC logLik deviance df.resid
> 62325.9 62506.9 -31134.9 62269.9 4716
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -24.3783 -0.1551 -0.0074 0.1392 12.5288
>
> Random effects:
> Groups Name Variance Std.Dev. Corr
> id (Intercept) 4.681e+04 2.164e+02
> t 7.925e+00 2.815e+00 1.00
> I(t^2) 2.559e-05 5.059e-03 -0.87 -0.87
> stim.L 1.591e+05 3.989e+02 -0.12 -0.12 0.17
> t:stim.L 1.105e+00 1.051e+00 -0.58 -0.58 0.78 0.33
> I(t^2):stim.L 2.367e-05 4.865e-03 0.06 0.06 -0.21
> -0.76 -0.45
> Residual 2.049e+04 1.432e+02
> Number of obs: 4744, groups: id, 97
>
> Fixed effects:
> Estimate Std. Error t value
> (Intercept) 2.960e+04 1.637e+02 180.85
> t 1.291e+01 8.493e-01 15.20
> I(t^2) -1.579e-02 1.110e-03 -14.21
> stim.L -3.956e+03 2.329e+02 -16.98
> t:stim.L 2.047e+01 1.136e+00 18.01
> I(t^2):stim.L -2.477e-02 1.478e-03 -16.76
>
> Correlation of Fixed Effects:
> (Intr) t I(t^2) stim.L t:st.L
> t -0.886
> I(t^2) 0.811 -0.966
> stim.L 0.972 -0.930 0.868
> t:stim.L -0.989 0.911 -0.826 -0.973
> I(t^2):st.L 0.917 -0.858 0.761 0.870 -0.947
>
> The fit of the model is quite good (pseudo r2 is 0.96), but have some
> problems:
> 1: quite “extreme” residuals (-24.3783, 12.5288)
> 2: quite high correlations among random effects
> 3: lousy qqplot (apart from the perfect fit on the from -2 to +2 std
> normal quantiles)
>
> Help please? What is wrong with the model (something is, I’m sure).
>
>
>
>
> --
> Marko Tončić, PhD
> Postdoctoral research assistant
> University of Rijeka
> Faculty of Humanities and Social Sciences
> Department of Psychology
> Sveucilisna avenija 4, 51000 Rijeka, CROATIA
> e-mail: mtoncic using ffri.hr <mailto:mtoncic using ffri.hr>
>
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--
Marko Tončić, PhD
Postdoctoral research assistant
University of Rijeka
Faculty of Humanities and Social Sciences
Department of Psychology
Sveucilisna avenija 4, 51000 Rijeka, CROATIA
e-mail: mtoncic using ffri.hr
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