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
Source |
SS |
DF |
MS |
F |
Sig of F |
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WITHIN+RESIDUAL |
33.81 |
5 |
6.76 |
|
|
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REGRESSION |
173.11 |
1 |
173.11 |
25.60 |
.004 |
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GROUP |
5.09 |
1 |
5.09 |
.75 |
.425 |
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Regression analysis for WITHIN+RESIDUAL error term --- Individual Univariate .9500 confidence intervals Dependent variable .. T4
COVARIATE |
B |
Beta |
Std. Err. |
t-Value |
Sig of t |
Lower -95% |
CL-Upper |
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T4 |
1.398 |
1.054 |
0.276 |
5.06 |
.004 |
0.6878 |
2.108 |
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Tests involving 'TRIAL' Within-Subject Effect.
- AVERAGED Tests of Significance for dv using UNIQUE sums of square
Source |
SS |
DF |
MS |
F |
Sig of F |
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WITHIN+RESIDUAL |
24.51 |
11 |
2.23 |
|
|
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REGRESSION |
.33 |
1 |
.33 |
.15 |
.709 |
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TRIAL |
45.94 |
2 |
22.97 |
10.31 |
.003 |
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GROUP BY TRIAL |
3.27 |
2 |
1.63 |
.73 |
.502 |
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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).Source |
Num df |
Denom DF |
F |
Sig of F |
|
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Intercept |
1 |
12.80 |
27.75 |
.000 |
|
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group |
1 |
5.881 |
2.177 |
.191 |
|
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trial |
2 |
10.858 |
12.708 |
.001 |
|
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group by trial |
2 |
10.287 |
0.704 |
.517 |
|
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cv |
1 |
12.24 |
0.081 |
.780 |
|
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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.