[R-sig-ME] Fwd: Linear Mixed-Effects Models - lme() command

[Domenico Di Carlo]

---------- Forwarded message ----------
From: Domenico Di Carlo <pvt.math82 at gmail.com>
Date: 2013/8/6
Subject: Linear Mixed-Effects Models - lme() command
To: bates at stat.wisc.edu


Dear Mr. Douglas Bates,
I have some questions about Linear Fixed Effects Models and about
*lme()*command of
*nlme* library of *R*.
This is dataset (called D) structure

*'data.frame':   187 obs. of  5 variables:*
* $ ID    : num  2492 2492 2492 2492 2492 ...*
* $ Cat1  : Factor w/ 3 levels "One","three",..: 2 2 2 2 2 2 2 2 2 2 ...*
* $ Cat2  : Factor w/ 3 levels "first","second",..: 1 1 1 1 1 1 1 1 1 1 ...*
* $ Values: num  253 320 424 432 476 434 527 476 468 544 ...*
* $ time  : num  0 1 1 1 1 1 2 2 2 3 ...*

The aim is to undestand *Values* changes in *Cat1* and *Cat2* levels across
the *time*. The line command I have used is:

*> library(nlme)*
*> model_1<-lme(Values~time:Cat1+time:Cat2,*
*+ random=~1|ID, data=D)*
*> summary(model_1)*
*Linear mixed-effects model fit by REML*
* Data: D *
*      AIC      BIC    logLik*
*  2295.15 2320.738 -1139.575*
*
*
*Random effects:*
* Formula: ~1 | ID*
*        (Intercept) Residual*
*StdDev:     107.022 114.4641*
*
*
*Fixed effects: Values ~ time:Cat1 + time:Cat2 *
*                       Value Std.Error  DF   t-value p-value*
*(Intercept)         324.0124  43.49774 175  7.448947  0.0000*
*time:Cat1One         51.4522  17.16804 175  2.996976  0.0031*
*time:Cat1three       47.0102   8.56644 175  5.487712  0.0000*
*time:Cat1two         69.5621  15.68291 175  4.435532  0.0000*
*time:Cat2[T.second] -24.4386  13.75771 175 -1.776360  0.0774*
*time:Cat2[T.third]  -21.3869  19.35976 175 -1.104710  0.2708*
* Correlation: *
*                    (Intr) tm:C1O tm:Ct1th tm:Ct1tw tm:Ct2[T.s]*
*time:Cat1One        -0.084                                     *
*time:Cat1three      -0.191  0.497                              *
*time:Cat1two        -0.104  0.711  0.546                       *
*time:Cat2[T.second]  0.026 -0.803 -0.605   -0.879              *
*time:Cat2[T.third]   0.018 -0.882 -0.430   -0.625    0.711     *
*
*
*Standardized Within-Group Residuals:*
*       Min         Q1        Med         Q3        Max *
*-3.0730790 -0.4341496  0.0301899  0.4023551  5.4252466 *
*
*
*Number of Observations: 187*
*Number of Groups: 7 *

About *time:Cat1One*, *time:Cat1three* and *time:Cat1two*, I guess (maybe
you can correct me) they are slopes of *Cat1* levels, I mean the average
increase of *Value* year after year. About *time:Cat2[T.second]* and *
time:Cat[T.third]*, I guess they are differences from slope of dummy of *
Cat2*, I mean *first* level of the variable. But to understand the real
meaning of this difference, I need to see the real value of *
time:Cat[T.first]*. Is it possible to see it? I was thinking that maybe
this value is the *intercept*, but its value *(324.0124)* is not the
estimate I was waiting for.
I have fitted a second model:

*> model_2<-lme(Values~time*Cat1+time*Cat2,*
*+ random=~1|ID, data=D)*
*> summary(model_2)*
*Linear mixed-effects model fit by REML*
* Data: D *
*       AIC      BIC    logLik*
*  2253.048 2291.162 -1114.524*
*
*
*Random effects:*
* Formula: ~1 | ID*
*        (Intercept) Residual*
*StdDev:    100.3245 114.4606*
*
*
*Fixed effects: Values ~ time * Cat1 + time * Cat2 *
*                        Value Std.Error  DF    t-value p-value*
*(Intercept)         200.91095 171.01061 175  1.1748450  0.2417*
*time                 54.11604  17.93540 175  3.0172746  0.0029*
*Cat1[T.three]       150.09485 151.92072   2  0.9879814  0.4273*
*Cat1[T.two]         270.12004 131.59306   2  2.0526921  0.1765*
*Cat2[T.second]      -44.75005 133.55838   2 -0.3350599  0.7695*
*Cat2[T.third]        58.30254 202.25915   2  0.2882566  0.8003*
*time:Cat1[T.three]   -8.11917  15.53307 175 -0.5227025  0.6018*
*time:Cat1[T.two]     10.91819  13.08954 175  0.8341161  0.4054*
*time:Cat2[T.second] -22.90242  14.49702 175 -1.5798018  0.1160*
*time:Cat2[T.third]  -22.43406  20.29314 175 -1.1054997  0.2705*
* Correlation: *
*                    (Intr) time   Ct1[T.th] Ct1[T.tw] Ct2[T.s] Ct2[T.t]*
*time                -0.314                                             *
*Cat1[T.three]       -0.888  0.259                                      *
*Cat1[T.two]         -0.507  0.136  0.571                               *
*Cat2[T.second]      -0.781  0.268  0.575     0.000                     *
*Cat2[T.third]       -0.846  0.265  0.751     0.429     0.660           *
*time:Cat1[T.three]   0.265 -0.866 -0.299    -0.157    -0.185   -0.224  *
*time:Cat1[T.two]     0.143 -0.475 -0.161    -0.298     0.000   -0.121  *
*time:Cat2[T.second]  0.259 -0.808 -0.175     0.000    -0.332   -0.219  *
*time:Cat2[T.third]   0.277 -0.884 -0.229    -0.120    -0.237   -0.314  *
*                    tm:Ct1[T.th] tm:Ct1[T.tw] tm:Ct2[T.s]*
*time                                                     *
*Cat1[T.three]                                            *
*Cat1[T.two]                                              *
*Cat2[T.second]                                           *
*Cat2[T.third]                                            *
*time:Cat1[T.three]                                       *
*time:Cat1[T.two]     0.548                               *
*time:Cat2[T.second]  0.576        0.000                  *
*time:Cat2[T.third]   0.765        0.420        0.714     *
*
*
*Standardized Within-Group Residuals:*
*        Min          Q1         Med          Q3         Max *
*-3.19403849 -0.41767624  0.03823682  0.44202369  5.35682026 *
*
*
*Number of Observations: 187*
*Number of Groups: 7 *

In this last model, I guess interactions terms differences are related to
the term *time*, but I do not understand if this term is the dummy of *Cat1*or
*Cat2*.
I am sorry if I have written something wrong, I hope you can help me to
understand my doubts. I am sending to you all the materials.
Best regards
Domenico Di Carlo