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The experiment: Two groups of children perform tasks with three levels of difficulty at two different time points and brain activity is measured. All of the children perform all of the tasks and do so at both timepoints.

Dependent variable: Brain Activity (BA)
Repeated measures: task (three levels), time (2 levels)
Independent: Group
Covariate: Age

I have been using a repeated measures ANCOVA to analyse the data but recently have attempted a mixed model for increased flexibility in contrasts / post hoc options. A 3 way interaction that is meaningful to me, group x task x time, is significant with the ANCOVA method but not with the mixed model, even when modeling the same main effects and interactions. The syntax (SPSS) for each model is below. I am concerned that I am using the mixed model incorrectly. Does anyone know what I could do differently with my mixed model to make it more similar to what I have done with the ANCOVA?

DATASET ACTIVATE DataSet1. 
GLM Time1Task1 Time1Task2 Time1Task3 Time2Task1 Time2Task2 Time2Task3 BY Group WITH Age 
  /WSFACTOR=fixation 2 Polynomial target 3 Polynomial 
  /METHOD=SSTYPE(3) 
  /CRITERIA=ALPHA(.05) 
  /WSDESIGN= task time task*time 
  /DESIGN= Group Age.

MIXED EEG BY Group Time Task WITH Age 
  /CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE) 
  /FIXED=Group*Time*Task Task Time Time*Age Group*Task Group*Time Task*Age Time*Task Time*Task*Age | SSTYPE(3) 
  /METHOD=REML 
  /RANDOM=INTERCEPT Age | SUBJECT(id) COVTYPE(UN) 
  /REPEATED=Target*Time | SUBJECT(id) COVTYPE(UN).

In the ANCOVA, the tests of within subjects effects table ends up having 9 effects. I have specified the same 9 effects in the mixed model. I realize this is a rather ridiculously large number of interactions included in the mixed model, but I wanted to mirror what the ANCOVA gives me (it is not possible to get an output for task x time x age in the GLM unless I include all of the above interactions - the model is only customizable within "within subject" factors and within "between subject" factors and then it automatically includes all interactions between "within" and "between" subject factors.

I have played around with:

  • not including random effects (age, subject ID)
  • including less effects in the mixed model while still including the interaction of interest, task x time x age
  • different covariance matrices

And none of these things mean that the task x time x age interaction is significant. I am concerned that there is something fundamentally wrong about the way I have depicted repeated measures testing with a covariate in the mixed model rather than these minor adjustments.

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  • $\begingroup$ Update: I broke the analysis down into very small pieces. When I have only one repeated factor (eg. time instead of time and task) the analysis comes out the same for ANCOVA and mixed model. It must have something to do with how mixed model treats the data when two repeated measures are present. $\endgroup$ – user27128 Jun 24 '13 at 13:12

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