strange model fit- help
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 INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND FOREST Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be> Havenlaan 88 bus 73, 1000 Brussel www.inbo.be <http://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 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 /////////////////////////////////////////////////////////////////////////////////////////// <https://www.inbo.be> Op za 14 mrt. 2020 om 17:10 schreef marKo via R-sig-mixed-models <r-sig-mixed-models at r-project.org <mailto:r-sig-mixed-models at 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 Ton?i?, 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 at ffri.hr <mailto:mtoncic at ffri.hr>
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Marko Ton?i?, 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 at ffri.hr