I think that these models are not nested and thus the LRT produced by anova.lme() will not be valid; AIC and BIC could be more relevant. In terms of interpretability, I'd say that a model treating 'zeitn' as a factor is much easier to explain than a model with 4th order polynomial.
I hope it helps. Best, Dimitris ---- Dimitris Rizopoulos Ph.D. Student Biostatistical Centre School of Public Health Catholic University of Leuven Address: Kapucijnenvoer 35, Leuven, Belgium Tel: +32/(0)16/336899 Fax: +32/(0)16/337015 Web: http://www.med.kuleuven.be/biostat/ http://www.student.kuleuven.be/~m0390867/dimitris.htm ----- Original Message ----- From: "Leo Gürtler" <[EMAIL PROTECTED]> To: <r-help@stat.math.ethz.ch> Sent: Monday, January 09, 2006 2:59 PM Subject: [R] decide between polynomial vs ordered factor model (lme) > Dear alltogether, > > two lme's, the data are available at: > > http://www.anicca-vijja.de/lg/hlm3_nachw.Rdata > > explanations of the data: > > nachw = post hox knowledge tests over 6 measure time points (= > equally > spaced) > zeitn = time points (n = 6) > subgr = small learning groups (n = 28) > gru = 4 different groups = treatment factor > > levels: time (=zeitn) (n=6) within subject (n=4) within smallgroups > (=gru) (n = 28), i.e. n = 4 * 28 = 112 persons and 112 * 6 = 672 > data points > > library(nlme) > fitlme7 <- lme(nachw ~ I(zeitn-3.5) + I((zeitn-3.5)^2) + > I((zeitn-3.5)^3) + I((zeitn-3.5)^4)*gru, random = list(subgr = ~ 1, > subject = ~ zeitn), data = hlm3) > > fit5 <- lme(nachw ~ ordered(I(zeitn-3.5))*gru, random = list(subgr = > ~ 1, subject = ~ zeitn), data = hlm3) > > anova( update(fit5, method="ML"), update(fitlme7, method="ML") ) > > > anova( update(fit5, method="ML"), update(fitlme7, method="ML") ) > Model df AIC BIC logLik > Test > update(fit5, method = "ML") 1 29 2535.821 2666.619 -1238.911 > update(fitlme7, method = "ML") 2 16 2529.719 2601.883 -1248.860 > 1 vs 2 > L.Ratio p-value > update(fit5, method = "ML") > update(fitlme7, method = "ML") 19.89766 0.0978 > > > > shows that both are ~ equal, although I know about the uncertainty > of ML > tests with lme(). Both models show that the ^2 and the ^4 terms are > important parts of the model. > > My question is: > > - Is it legitim to choose a model based on these outputs according > to > theoretical considerations instead of statistical tests that not > really > show a superiority of one model over the other one? > > - Is there another criterium I've overseen to decide which model can > be > clearly prefered? > > - The idea behind that is that in the one model (fit5) the second > contrast of the factor (gru) is statistically significant, although > not > the whole factor in the anova output. > In the other model, this is not the case. > Theoretically interesting is of course the significance of the > second > contrast of gru, as it shows a tendency of one treatment being > slightly > superior. I want to choose this model but I am not sure whether this > is > proper action. Both models shows this trend, but only one model > clearly > indicates that this trend bears some empirical meaning. > > Thanks for any suggestions, > > leo > > > here are the outputs for each model: > >> fitlme7 <- lme(nachw ~ I(zeitn-3.5) + I((zeitn-3.5)^2) + > I((zeitn-3.5)^3) + I((zeitn-3.5)^4)*gru, random = list(subgr = ~ 1, > subject = ~ zeitn), data = hlm3) >> plot(augPred(fitlme7), layout=c(14,8)) >> summary(fitlme7); anova(fitlme7); intervals(fitlme7) > Linear mixed-effects model fit by REML > Data: hlm3 > AIC BIC logLik > 2582.934 2654.834 -1275.467 > > Random effects: > Formula: ~1 | subgr > (Intercept) > StdDev: 0.5833797 > > Formula: ~zeitn | subject %in% subgr > Structure: General positive-definite, Log-Cholesky parametrization > StdDev Corr > (Intercept) 0.6881908 (Intr) > zeitn 0.1936087 -0.055 > Residual 1.3495785 > > Fixed effects: nachw ~ I(zeitn - 3.5) + I((zeitn - 3.5)^2) + > I((zeitn - > 3.5)^3) + I((zeitn - 3.5)^4) * gru > Value Std.Error DF t-value p-value > (Intercept) 4.528757 0.17749012 553 25.515542 0.0000 > I(zeitn - 3.5) 0.010602 0.08754449 553 0.121100 0.9037 > I((zeitn - 3.5)^2) 0.815693 0.09765075 553 8.353171 0.0000 > I((zeitn - 3.5)^3) 0.001336 0.01584169 553 0.084329 0.9328 > I((zeitn - 3.5)^4) -0.089655 0.01405811 553 -6.377486 0.0000 > gru1 0.187181 0.30805090 24 0.607630 0.5491 > gru2 0.532665 0.30805090 24 1.729147 0.0966 > gru3 -0.046305 0.30805090 24 -0.150317 0.8818 > I((zeitn - 3.5)^4):gru1 -0.007860 0.00600928 553 -1.307993 0.1914 > I((zeitn - 3.5)^4):gru2 -0.001259 0.00600928 553 -0.209516 0.8341 > I((zeitn - 3.5)^4):gru3 -0.000224 0.00600928 553 -0.037225 0.9703 > Correlation: > (Intr) I(-3.5 I((-3.5)^2 I((-3.5)^3 > I((z-3.5)^4) > I(zeitn - 3.5) 0.071 > I((zeitn - 3.5)^2) -0.465 0.000 > I((zeitn - 3.5)^3) 0.000 -0.914 0.000 > I((zeitn - 3.5)^4) 0.401 0.000 -0.977 0.000 > gru1 0.000 0.000 0.000 0.000 0.000 > gru2 0.000 0.000 0.000 0.000 0.000 > gru3 0.000 0.000 0.000 0.000 0.000 > I((zeitn - 3.5)^4):gru1 0.000 0.000 0.000 0.000 0.000 > I((zeitn - 3.5)^4):gru2 0.000 0.000 0.000 0.000 0.000 > I((zeitn - 3.5)^4):gru3 0.000 0.000 0.000 0.000 0.000 > gru1 gru2 gru3 I((-3.5)^4):1 > I((-3.5)^4):2 > I(zeitn - 3.5) > I((zeitn - 3.5)^2) > I((zeitn - 3.5)^3) > I((zeitn - 3.5)^4) > gru1 > gru2 0.000 > gru3 0.000 0.000 > I((zeitn - 3.5)^4):gru1 -0.287 0.000 0.000 > I((zeitn - 3.5)^4):gru2 0.000 -0.287 0.000 0.000 > I((zeitn - 3.5)^4):gru3 0.000 0.000 -0.287 0.000 0.000 > > Standardized Within-Group Residuals: > Min Q1 Med Q3 Max > -3.1326192 -0.5888543 0.0239228 0.6519002 2.1238820 > > Number of Observations: 672 > Number of Groups: > subgr subject %in% subgr > 28 112 > numDF denDF F-value p-value > (Intercept) 1 553 1426.5275 <.0001 > I(zeitn - 3.5) 1 553 0.2381 0.6258 > I((zeitn - 3.5)^2) 1 553 98.6712 <.0001 > I((zeitn - 3.5)^3) 1 553 0.0071 0.9328 > I((zeitn - 3.5)^4) 1 553 40.6723 <.0001 > gru 3 24 1.0410 0.3924 > I((zeitn - 3.5)^4):gru 3 553 0.5854 0.6248 > Approximate 95% confidence intervals > > Fixed effects: > lower est. upper > (Intercept) 4.18011938 4.5287566579 4.877393940 > I(zeitn - 3.5) -0.16135875 0.0106016498 0.182562052 > I((zeitn - 3.5)^2) 0.62388162 0.8156933820 1.007505144 > I((zeitn - 3.5)^3) -0.02978133 0.0013359218 0.032453178 > I((zeitn - 3.5)^4) -0.11726922 -0.0896553959 -0.062041570 > gru1 -0.44860499 0.1871808283 0.822966643 > gru2 -0.10312045 0.5326653686 1.168451183 > gru3 -0.68209096 -0.0463051419 0.589480673 > I((zeitn - 3.5)^4):gru1 -0.01966389 -0.0078600880 0.003943709 > I((zeitn - 3.5)^4):gru2 -0.01306284 -0.0012590380 0.010544759 > I((zeitn - 3.5)^4):gru3 -0.01202749 -0.0002236923 0.011580105 > attr(,"label") > [1] "Fixed effects:" > > Random Effects: > Level: subgr > lower est. upper > sd((Intercept)) 0.3459779 0.5833797 0.9836812 > Level: subject > lower est. upper > sd((Intercept)) 0.4388885 0.68819079 1.0791046 > sd(zeitn) 0.1320591 0.19360866 0.2838449 > cor((Intercept),zeitn) -0.4835884 -0.05541043 0.3941661 > > Within-group standard error: > lower est. upper > 1.267548 1.349579 1.436918 > > ######################################################### > an the other model: > >> summary(fit5); anova(fit5); intervals(fit5) > Linear mixed-effects model fit by REML > Data: hlm3 > AIC BIC logLik > 2564.135 2693.878 -1253.067 > > Random effects: > Formula: ~1 | subgr > (Intercept) > StdDev: 0.5833753 > > Formula: ~zeitn | subject %in% subgr > Structure: General positive-definite, Log-Cholesky parametrization > StdDev Corr > (Intercept) 0.6453960 (Intr) > zeitn 0.1709843 0.13 > Residual 1.3497627 > > Fixed effects: nachw ~ ordered(I(zeitn - 3.5)) + gru + > ordered(I(zeitn - > 3.5)):gru > Value Std.Error DF t-value > p-value > (Intercept) 5.587313 0.1505852 540 37.10400 > 0.0000 > ordered(I(zeitn - 3.5)).L 0.072572 0.1443422 540 0.50278 > 0.6153 > ordered(I(zeitn - 3.5)).Q 1.266731 0.1275406 540 9.93198 > 0.0000 > ordered(I(zeitn - 3.5)).C 0.010754 0.1275406 540 0.08432 > 0.9328 > ordered(I(zeitn - 3.5))^4 -0.813277 0.1275406 540 -6.37662 > 0.0000 > ordered(I(zeitn - 3.5))^5 0.070373 0.1275406 540 0.55177 > 0.5813 > gru1 0.056700 0.3011704 24 0.18826 > 0.8523 > gru2 0.679057 0.3011704 24 2.25473 > 0.0335 > gru3 -0.141425 0.3011704 24 -0.46958 > 0.6429 > ordered(I(zeitn - 3.5)).L:gru1 -0.070352 0.2886844 540 -0.24370 > 0.8076 > ordered(I(zeitn - 3.5)).Q:gru1 -0.360380 0.2550812 540 -1.41281 > 0.1583 > ordered(I(zeitn - 3.5)).C:gru1 -0.162411 0.2550812 540 -0.63670 > 0.5246 > ordered(I(zeitn - 3.5))^4:gru1 0.086343 0.2550812 540 0.33849 > 0.7351 > ordered(I(zeitn - 3.5))^5:gru1 -0.017207 0.2550812 540 -0.06746 > 0.9462 > ordered(I(zeitn - 3.5)).L:gru2 0.788896 0.2886844 540 2.73273 > 0.0065 > ordered(I(zeitn - 3.5)).Q:gru2 0.033386 0.2550812 540 0.13089 > 0.8959 > ordered(I(zeitn - 3.5)).C:gru2 0.089757 0.2550812 540 0.35188 > 0.7251 > ordered(I(zeitn - 3.5))^4:gru2 -0.402616 0.2550812 540 -1.57839 > 0.1151 > ordered(I(zeitn - 3.5))^5:gru2 -0.507855 0.2550812 540 -1.99095 > 0.0470 > ordered(I(zeitn - 3.5)).L:gru3 -0.439200 0.2886844 540 -1.52138 > 0.1287 > ordered(I(zeitn - 3.5)).Q:gru3 0.026105 0.2550812 540 0.10234 > 0.9185 > ordered(I(zeitn - 3.5)).C:gru3 -0.273643 0.2550812 540 -1.07277 > 0.2839 > ordered(I(zeitn - 3.5))^4:gru3 -0.163738 0.2550812 540 -0.64191 > 0.5212 > ordered(I(zeitn - 3.5))^5:gru3 0.204174 0.2550812 540 0.80043 > 0.4238 > Correlation: > (Intr) or(I(-3.5)).L or(I(-3.5)).Q > or(I(-3.5)).C or(I(-3.5))^4 or(I(-3.5))^5 gru1 gru2 gru3 > o(I(-3.5)).L:1 > o(I(-3.5)).Q:1 o(I(-3.5)).C:1 > ordered(I(zeitn - 3.5)).L > 0.2 > > > ordered(I(zeitn - 3.5)).Q 0.0 > 0.0 > > > ordered(I(zeitn - 3.5)).C 0.0 0.0 > 0.0 > > > ordered(I(zeitn - 3.5))^4 0.0 0.0 0.0 > 0.0 > > > ordered(I(zeitn - 3.5))^5 0.0 0.0 0.0 > 0.0 > 0.0 > > > gru1 0.0 0.0 0.0 > 0.0 0.0 > 0.0 > gru2 0.0 0.0 0.0 > 0.0 0.0 0.0 > 0.0 > gru3 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 > 0.0 > ordered(I(zeitn - 3.5)).L:gru1 0.0 0.0 0.0 > 0.0 0.0 0.0 0.2 0.0 > 0.0 > ordered(I(zeitn - 3.5)).Q:gru1 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 > ordered(I(zeitn - 3.5)).C:gru1 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 > ordered(I(zeitn - 3.5))^4:gru1 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5))^5:gru1 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).L:gru2 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.2 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).Q:gru2 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).C:gru2 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5))^4:gru2 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5))^5:gru2 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).L:gru3 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.2 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).Q:gru3 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).C:gru3 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5))^4:gru3 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5))^5:gru3 0.0 0.0 0.0 > 0.0 0.0 0.0 0.0 0.0 0.0 0.0 > 0.0 0.0 > o(I(-3.5))^4:1 o(I(-3.5))^5:1 > o(I(-3.5)).L:2 o(I(-3.5)).Q:2 o(I(-3.5)).C:2 o(I(-3.5))^4:2 > o(I(-3.5))^5:2 o(I(-3.5)).L:3 o(I(-3.5)).Q:3 > ordered(I(zeitn - > 3.5)).L > > > ordered(I(zeitn - > 3.5)).Q > > > ordered(I(zeitn - > 3.5)).C > > > ordered(I(zeitn - > 3.5))^4 > > > ordered(I(zeitn - > 3.5))^5 > > > gru1 > > > > gru2 > > > > gru3 > > > > ordered(I(zeitn - > 3.5)).L:gru1 > > > ordered(I(zeitn - > 3.5)).Q:gru1 > > > ordered(I(zeitn - > 3.5)).C:gru1 > > > ordered(I(zeitn - > 3.5))^4:gru1 > > > ordered(I(zeitn - 3.5))^5:gru1 > 0.0 > > > ordered(I(zeitn - 3.5)).L:gru2 0.0 > 0.0 > > > ordered(I(zeitn - 3.5)).Q:gru2 0.0 0.0 > 0.0 > > > ordered(I(zeitn - 3.5)).C:gru2 0.0 0.0 > 0.0 > 0.0 > > > ordered(I(zeitn - 3.5))^4:gru2 0.0 0.0 > 0.0 0.0 > 0.0 > ordered(I(zeitn - 3.5))^5:gru2 0.0 0.0 > 0.0 0.0 0.0 > 0.0 > ordered(I(zeitn - 3.5)).L:gru3 0.0 0.0 > 0.0 0.0 0.0 0.0 > 0.0 > ordered(I(zeitn - 3.5)).Q:gru3 0.0 0.0 > 0.0 0.0 0.0 0.0 > 0.0 0.0 > ordered(I(zeitn - 3.5)).C:gru3 0.0 0.0 > 0.0 0.0 0.0 0.0 > 0.0 0.0 0.0 > ordered(I(zeitn - 3.5))^4:gru3 0.0 0.0 > 0.0 0.0 0.0 0.0 > 0.0 0.0 0.0 > ordered(I(zeitn - 3.5))^5:gru3 0.0 0.0 > 0.0 0.0 0.0 0.0 > 0.0 0.0 0.0 > o(I(-3.5)).C:3 o(I(-3.5))^4:3 > ordered(I(zeitn - 3.5)).L > ordered(I(zeitn - 3.5)).Q > ordered(I(zeitn - 3.5)).C > ordered(I(zeitn - 3.5))^4 > ordered(I(zeitn - 3.5))^5 > gru1 > gru2 > gru3 > ordered(I(zeitn - 3.5)).L:gru1 > ordered(I(zeitn - 3.5)).Q:gru1 > ordered(I(zeitn - 3.5)).C:gru1 > ordered(I(zeitn - 3.5))^4:gru1 > ordered(I(zeitn - 3.5))^5:gru1 > ordered(I(zeitn - 3.5)).L:gru2 > ordered(I(zeitn - 3.5)).Q:gru2 > ordered(I(zeitn - 3.5)).C:gru2 > ordered(I(zeitn - 3.5))^4:gru2 > ordered(I(zeitn - 3.5))^5:gru2 > ordered(I(zeitn - 3.5)).L:gru3 > ordered(I(zeitn - 3.5)).Q:gru3 > ordered(I(zeitn - 3.5)).C:gru3 > ordered(I(zeitn - 3.5))^4:gru3 0.0 > ordered(I(zeitn - 3.5))^5:gru3 0.0 0.0 > > Standardized Within-Group Residuals: > Min Q1 Med Q3 Max > -3.10206117 -0.62626454 0.02807962 0.64554138 2.13155536 > > Number of Observations: 672 > Number of Groups: > subgr subject %in% subgr > 28 112 > numDF denDF F-value p-value > (Intercept) 1 540 1426.5315 <.0001 > ordered(I(zeitn - 3.5)) 5 540 27.9740 <.0001 > gru 3 24 1.0410 0.3924 > ordered(I(zeitn - 3.5)):gru 15 540 1.4115 0.1363 > Approximate 95% confidence intervals > > Fixed effects: > lower est. upper > (Intercept) 5.2915086 5.58731309 5.883117621 > ordered(I(zeitn - 3.5)).L -0.2109689 0.07257212 0.356113124 > ordered(I(zeitn - 3.5)).Q 1.0161942 1.26673073 1.517267227 > ordered(I(zeitn - 3.5)).C -0.2397825 0.01075396 0.261290456 > ordered(I(zeitn - 3.5))^4 -1.0638138 -0.81327731 -0.562740815 > ordered(I(zeitn - 3.5))^5 -0.1801634 0.07037312 0.320909612 > gru1 -0.5648856 0.05669953 0.678284624 > gru2 0.0574723 0.67905739 1.300642487 > gru3 -0.7630097 -0.14142458 0.480160517 > ordered(I(zeitn - 3.5)).L:gru1 -0.6374343 -0.07035232 0.496729683 > ordered(I(zeitn - 3.5)).Q:gru1 -0.8614532 -0.36038020 0.140692783 > ordered(I(zeitn - 3.5)).C:gru1 -0.6634839 -0.16241093 0.338662057 > ordered(I(zeitn - 3.5))^4:gru1 -0.4147301 0.08634286 0.587415843 > ordered(I(zeitn - 3.5))^5:gru1 -0.5182803 -0.01720729 0.483865692 > ordered(I(zeitn - 3.5)).L:gru2 0.2218139 0.78889594 1.355977946 > ordered(I(zeitn - 3.5)).Q:gru2 -0.4676866 0.03338637 0.534459352 > ordered(I(zeitn - 3.5)).C:gru2 -0.4113159 0.08975711 0.590830099 > ordered(I(zeitn - 3.5))^4:gru2 -0.9036894 -0.40261640 0.098456584 > ordered(I(zeitn - 3.5))^5:gru2 -1.0089275 -0.50785453 -0.006781542 > ordered(I(zeitn - 3.5)).L:gru3 -1.0062815 -0.43919953 0.127882479 > ordered(I(zeitn - 3.5)).Q:gru3 -0.4749680 0.02610502 0.527178001 > ordered(I(zeitn - 3.5)).C:gru3 -0.7747163 -0.27364336 0.227429629 > ordered(I(zeitn - 3.5))^4:gru3 -0.6648114 -0.16373838 0.337334604 > ordered(I(zeitn - 3.5))^5:gru3 -0.2968991 0.20417390 0.705246883 > attr(,"label") > [1] "Fixed effects:" > > Random Effects: > Level: subgr > lower est. upper > sd((Intercept)) 0.3464888 0.5833753 0.9822158 > Level: subject > lower est. upper > sd((Intercept)) 0.3640439 0.6453960 1.1441916 > sd(zeitn) 0.1000264 0.1709843 0.2922790 > cor((Intercept),zeitn) -0.6712236 0.1295558 0.7907922 > > Within-group standard error: > lower est. upper > 1.265702 1.349763 1.439406 > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html