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nlme vs aov with Error() for an ANCOVA

2 messages · Christoph Lehmann, Brian Ripley

Christoph Lehmann
# 
Hi 
I compouted a multiple linear regression with repeated measures on one
explanatory variable:
BOLD peak (blood oxygenation) as dependent variable,

and as independent variables I have:
-age.group (binaray:young(0)/old(1)) 
-and task-difficulty measured by means of the reaction-time 'rt'. For
'rt' I have repeated measurements, since each subject did 12 different
tasks.
-> so it can be seen as an ANCOVA

subject  age.group bold    rt

subj1    0         0.08    0.234   
subj1    0         0.05    0.124 
..  
subj1    0         0.07    0.743  
    
subj2    0         0.06    0.234     
subj2    0         0.02    0.183 
..    
subj2    0         0.05    0.532 
     
subjn    1         0.09    0.234    
subjn    1         0.06    0.155
..    
subjn    1         0.07    0.632      

I decided to use the nlme library:

patrizia.lme <- lme(bold ~ rt*age.group, data=patrizia.data1, random= ~
rt |subject)
Linear mixed-effects model fit by REML
 Data: patrizia.data1
       AIC      BIC    logLik
  272.2949 308.3650 -128.1474
 
Random effects:
 Formula: ~rt | subject
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev       Corr
(Intercept) 0.2740019518 (Intr)
rt          0.0004756026 -0.762
Residual    0.2450787149
 
Fixed effects: bold ~ rt + age.group + rt:age.group
                   Value  Std.Error  DF   t-value p-value
(Intercept)   0.06109373 0.11725208 628  0.521046  0.6025
rt            0.00110117 0.00015732 628  6.999501  0.0000
age.group    -0.03750787 0.13732793  43 -0.273126  0.7861
rt:age.group -0.00031919 0.00018259 628 -1.748115  0.0809
 Correlation:
             (Intr) rt     ag.grp
rt           -0.818
age.group    -0.854  0.698
rt:age.group  0.705 -0.862 -0.805
 
Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-3.6110596 -0.5982741 -0.0408144  0.5617381  4.8648242
 
Number of Observations: 675
Number of Groups: 45

--end output
#-> if the model assumptions hold this means, we don't have a
significant age effect but a highly significant task-effect and the
interaction is significant on the 0.1 niveau. 

I am now interested, if one could do the analysis also using aov and the
Error() option.

e.g. may I do:
Error: subject
   Df    Sum Sq   Mean Sq
rt  1 0.0022087 0.0022087
 
Error: subject:rt
   Df Sum Sq Mean Sq
rt  1 40.706  40.706
 
Error: Within
              Df  Sum Sq Mean Sq F value    Pr(>F)
rt             1   2.422   2.422 10.0508  0.001592 **
age.group      1   8.722   8.722 36.2022 2.929e-09 ***
rt:age.group   1   0.277   0.277  1.1494  0.284060
Residuals    669 161.187   0.241
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1


which looks weird

or what would you recommend?

thanks a lot

Christoph
Brian Ripley
# 
Well, I don't think this is ANCOVA as you seem to want to specify a random 
slope for a covariate.  aov() is not designed for that.  It is also not 
designed for assessing the size of fixed effects which seems the question 
here.

As I understand it, you have only one observation for each value of `rt'
for each subject, and `rt' is an explanatory variable.  For lme you have
specified a subject-dependent intercept and coefficient of `rt'.  You
cannot do that in aov, where the argument of Error is supposed to be a
factor or a combination of factors.  This is in the reference given by
help for aov or Error (on pp 157-9).
On Thu, 15 Jan 2004, Christoph Lehmann wrote:

            

      
      
      
    

        
Nope.  It means that you have two lines with a common non-zero intercept
and probably different slopes for the two age groups.  However, as I 
understand it rt=0 is an extraplolation to an physically impossible value, 
so interpreting the intercept makes little sense.