# decide between polynomial vs ordered factor model (lme)

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## 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.Rdataexplanations 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 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: decide between polynomial vs ordered factor model (lme)

 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" <[hidden email]> To: <[hidden email]> 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 > > ______________________________________________ > [hidden email] 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______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: decide between polynomial vs ordered factor model (lme)

 In reply to this post by Leo Gürtler On 1/9/06, Leo Gürtler <[hidden email]> wrote: > 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 legitimate 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 overlooked to decide which model can be > clearly preferred? > > - 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, The comparisons may be more clearly shown if you create the ordered factor and a second version of the ordered factor what has the contrasts set so it produces a 4th order polynomial.  That is, set hlm3\$ozeit <- ordered(hlm3\$zeitn) hlm3\$ozeit4 <- C(hlm3\$ozeit, contr.poly, 4) then define one model in terms of ozeit and a second model in terms of ozeit4. I would go further and create a new binary factor from gru that contrasted level 2 against the other three levels and use that instead of gru. For a model fit by lme I would use the one-argument form of anova to assess the significance of terms in the fixed effects.  (That advice doesn't hold for models fit by lmer - at least at present.) ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html