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 ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
