= Comparison of handling a varying covaruate (within subject) using SPSS MANOVA and SPSS MIXED =

We illustrate using the data below with one time factor df() with three time points wach with a different covariate value cv()

{{{
data list list
  / sub group dv1 dv2 dv3 cv1 cv2 cv3.
begin data.
1 1  3  4  7  3 1 2
2 1  6  8 12  9 3 1
3 1  7 13 11 11 8 4
4 1  0  3  6  6 2 1
5 2  5  6 11  7 8 3
6 2 10 12 18 15 9 5
7 2 10 15 15 14 8 6
8 2  5  7 11  9 2 8 
end data.
}}}

Using MANOVA
{{{
manova dv1 dv2 dv3 by group(1,2) with cv1 cv2 cv3
  /wsfactors trial (3)
  /wsdesign trial
  /design
}}}

we obtain

Tests of Significance for T1 using UNIQUE sums of squares

||||||||||||<style="TEXT-ALIGN: center"> '''Source''' || '''SS''' || '''DF''' || '''MS''' || '''F''' || Sig of F ||
||||||||||||<style="TEXT-ALIGN: center"> WITHIN+RESIDUAL || 33.81 || 5 || 6.76 ||  || ||
||||||||||||<style="TEXT-ALIGN: center"> REGRESSION || 173.11 || 1 || 173.11 || 25.60 || .004 ||
||||||||||||<style="TEXT-ALIGN: center"> GROUP || 5.09 || 1 || 5.09 || .75 || .425 ||



 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 Regression analysis for WITHIN+RESIDUAL error term

 --- Individual Univariate .9500 confidence intervals

 Dependent variable .. T4

||||||||||||||<style="TEXT-ALIGN: center"> '''COVARIATE''' || '''B''' || '''Beta''' || '''Std. Err.''' || '''t-Value''' || Sig of t || '''Lower -95%''' || '''CL-Upper''' ||
||||||||||||||<style="TEXT-ALIGN: center"> T4 || 1.398 || 1.054 || 0.276 || 5.06 || .004 || 0.6878 || 2.108 ||

Tests involving 'TRIAL' Within-Subject Effect. 
 
 AVERAGED Tests of Significance for dv using UNIQUE sums of square

||||||||||||<style="TEXT-ALIGN: center"> '''Source''' || '''SS''' || '''DF''' || '''MS''' || '''F''' || Sig of F ||
||||||||||||<style="TEXT-ALIGN: center"> WITHIN+RESIDUAL || 24.51 || 11 || 2.23 ||  || ||
||||||||||||<style="TEXT-ALIGN: center"> REGRESSION || .33 || 1 || .33 || .15 || .709 ||
||||||||||||<style="TEXT-ALIGN: center"> TRIAL || 45.94 || 2 || 22.97 || 10.31 || .003 ||
||||||||||||<style="TEXT-ALIGN: center"> GROUP BY TRIAL || 3.27 || 2 || 1.63 || .73 || .502 ||


We then need to reformat the data into 'long format' using the varstocases syntax and then fit the repeated measures data with varying covariate as a mixed model.

{{{ 
compute cvone=cv1.

varstocases
 /make dv from dv1 dv2 dv3
 /make cv from cv1 cv2 cv3
 /index = trial.
        
mixed dv by group trial with cv
  /fixed= group trial group*trial cv
  /repeated= trial | subject(sub) covtype(cs).
}}}

||||||||||||<style="TEXT-ALIGN: center"> '''Source''' || '''Num df''' || '''Denom DF''' || '''F''' || '''Sig of F''' ||  ||
||||||||||||<style="TEXT-ALIGN: center"> Intercept || 1 || 12.80 || 27.75 || .000 ||  ||
||||||||||||<style="TEXT-ALIGN: center"> group || 1 || 5.881 || 2.177 || .191 || ||
||||||||||||<style="TEXT-ALIGN: center"> trial || 2 || 10.858 || 12.708 || .001 || ||
||||||||||||<style="TEXT-ALIGN: center"> group by trial || 2 || 10.287 || 0.704 || .517 || ||
||||||||||||<style="TEXT-ALIGN: center"> cv || 1 || 12.24 || 0.081 || .780 || ||

 
The results using the two approaches are similar except for the group main effect which although non-significant in both has a lower significance level for the MANOVA.