R help - May 2013 - Changing Order of Factor Levels in Mixed Model (nlme)

R Help -

Why is that in the results below, changing the order of the factor
(trialType2: levels - DD, SD, DS, SS) changes the estimates in the fixed
effects tests?
> tmp.dat4$trialType2 <- sort(tmp.dat4$trialType, decreasing = TRUE)
> mod2c <- lme(proportion.down ~ trialType2, data = tmp.dat4, random = ~ 1
| subject, na.action = na.omit, method = "ML")
> summary(mod2c)
Linear mixed-effects model fit by maximum likelihood
 Data: tmp.dat4
       AIC      BIC    logLik
  27.92306 48.23003 -7.961531

Random effects:
 Formula: ~1 | subject
        (Intercept)  Residual
StdDev:   0.3800017 0.1530272

Fixed effects: proportion.down ~ trialType2
                  Value  Std.Error  DF   t-value p-value
(Intercept)   0.6788875 0.08613476 141  7.881690  0.0000
trialType2DS  0.0287062 0.11267357 141  0.254773  0.7993
trialType2SD -0.0197194 0.12142018 141 -0.162406  0.8712
trialType2SS -0.0941918 0.12204707 141 -0.771766  0.4415
 Correlation:
             (Intr) trT2DS trT2SD
trialType2DS -0.658
trialType2SD -0.709  0.467
trialType2SS -0.706  0.464  0.571

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-3.67176824 -0.22090663  0.08677971  0.14331603  2.86301670

Number of Observations: 218
Number of Groups: 74
> tmp.dat4$trialType2 <- sort(tmp.dat4$trialType, decreasing = FALSE)
> mod2c <- lme(proportion.down ~ trialType2, data = tmp.dat4, random = ~ 1
| subject, na.action = na.omit, method = "ML")
> summary(mod2c)
Linear mixed-effects model fit by maximum likelihood
 Data: tmp.dat4
       AIC      BIC    logLik
  27.92306 48.23003 -7.961531

Random effects:
 Formula: ~1 | subject
        (Intercept)  Residual
StdDev:   0.3800017 0.1530272

Fixed effects: proportion.down ~ trialType2
                 Value  Std.Error  DF  t-value p-value
(Intercept)  0.5846957 0.08646554 141 6.762181  0.0000
trialType2DS 0.0744724 0.11277773 141 0.660347  0.5101
trialType2SD 0.1228981 0.12175741 141 1.009368  0.3145
trialType2SS 0.0941918 0.12204707 141 0.771766  0.4415
 Correlation:
             (Intr) trT2DS trT2SD
trialType2DS -0.660
trialType2SD -0.710  0.469
trialType2SS -0.708  0.468  0.573

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-3.67176824 -0.22090663  0.08677971  0.14331603  2.86301670

Number of Observations: 218
Number of Groups: 74

-- 
*Edward H Patzelt | Research Assistant
Psychology | University of Minnesota  | Elliott Hall, 75 East River Road |
Minneapolis, MN 55455
Email: patze003@umn.edu  |
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Edward Patzelt <patze003 <at> umn.edu> writes:
> 
> R Help -
> 
> Why is that in the results below, changing the order of the factor
> (trialType2: levels - DD, SD, DS, SS) changes the estimates in the fixed
> effects tests?
  I think you're not doing what you expected.  By sorting the factor,
you are _not_ changing the order of the factor levels (which you might
have been trying to do in order to change the parameterization); rather,
you're changing the actual order of the observations of the factor,
which is scrambling their association with the other variables
(response=proportion.down and the grouping variable, subject).
  I can't think of a scenario under which sorting the order of only one
of the variables in the data frame is not a mistake, unless you're
trying to randomize the order to do a permutation test.

  What you might have meant to do is to change the order of
the _levels_ of the factor, which you can do via

tmp.dat4$trialType2 <- factor(tmp.dat4$trialType2,
                       
levels=c("DD","SD","DS","SS"))

or perhaps

tmp.dat4 <- transform(tmp.dat4,
   trialType2=factor(trialType2,levels=sort(levels(trialType2))))

(see also ?relevel and ?reorder)

  Changing the order of the factor levels will also change
the specific estimates of the fixed-effect parameters, in this
case by changing the parameterization (contrasts), which are
by default based on differences from the first factor level
(although see also ?contr.SAS), but not the overall meaning/fit
of the model.

  By the way, this isn't specifically a mixed-effects model
question -- the same issues would apply with just about any
statistical model in R (see e.g. Faraway's books on linear
and generalized models -- some early drafts are available in
the contributed documentation section).