### Stata FAQ How can I do multivariate repeated measures in Stata?

The manova command was added to Stata in version 8. Using the manova command along with transformations of the dependent variables will allow you to perform multivariate repeated measures analyses.

#### Example 1

The first example is a within-subjects design, also known as a randomized block design. There are four observations for each subject, labeled y1, y2, y3 and y4.
input s y1 y2 y3 y4
1  3  4  4  3
2  2  4  4  5
3  2  3  3  6
4  3  3  3  5
5  1  2  4  7
6  3  3  6  6
7  4  4  5 10
8  6  5  5  8
end
We need to create a variable to use as a constant and then run the manova with the noconstant option.
generate con = 1
manova y1 y2 y3 y4 = con, noconstant

Number of obs =       8

W = Wilks' lambda      L = Lawley-Hotelling trace
P = Pillai's trace     R = Roy's largest root

Source |  Statistic     df   F(df1,    df2) =   F   Prob>F
-----------+--------------------------------------------------
con | W   0.0196      1     4.0     4.0    49.92 0.0011 e
| P   0.9804            4.0     4.0    49.92 0.0011 e
| L  49.9217            4.0     4.0    49.92 0.0011 e
| R  49.9217            4.0     4.0    49.92 0.0011 e
|--------------------------------------------------
Residual |                 7
-----------+--------------------------------------------------
Total |                 8
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F
Next, we need to create contrasts among the dependent variables. If there are k dependent variables than we will create k-1 contrasts. These contrasts are created in a manner simmilar to that which is done with categorical predictors. We will create the contrasts using an effect coding.
mat ycomp = (1,0,0,-1\0,1,0,-1\0,0,1,-1)
mat list ycomp

ycomp[3,4]
c1  c2  c3  c4
r1   1   0   0  -1
r2   0   1   0  -1
r3   0   0   1  -1

manovatest con, ytrans(ycomp)

Transformations of the dependent variables
(1)    y1 - y4
(2)    y2 - y4
(3)    y3 - y4

W = Wilks' lambda      L = Lawley-Hotelling trace
P = Pillai's trace     R = Roy's largest root

Source |  Statistic     df   F(df1,    df2) =   F   Prob>F
-----------+--------------------------------------------------
con | W   0.2458      1     3.0     5.0     5.11 0.0554 e
| P   0.7542            3.0     5.0     5.11 0.0554 e
| L   3.0682            3.0     5.0     5.11 0.0554 e
| R   3.0682            3.0     5.0     5.11 0.0554 e
|--------------------------------------------------
Residual |                 7
---------------------------------------------------------
The F-test of 5.11 is the multivariate test of the within-subjects treatment. The result is not significant at the .05 level.

#### Example 2

This example will include one between-subjects factor with two levels. The design could be classified as a split-plot factorial.
input s a y1 y2 y3 y4
1 1 3 4 7  7
2 1 6 5 8  8
3 1 3 4 7  9
4 1 3 3 6  8
5 2 1 2 5 10
6 2 2 3 6 10
7 2 2 4 5  9
8 2 2 3 6 11
end
The first manova is a test of the between-subjects factor.
manova y1 y2 y3 y4 = a

Number of obs =       8

W = Wilks' lambda      L = Lawley-Hotelling trace
P = Pillai's trace     R = Roy's largest root

Source |  Statistic     df   F(df1,    df2) =   F   Prob>F
-----------+--------------------------------------------------
a | W   0.1374      1     4.0     3.0     4.71 0.1169 e
| P   0.8626            4.0     3.0     4.71 0.1169 e
| L   6.2764            4.0     3.0     4.71 0.1169 e
| R   6.2764            4.0     3.0     4.71 0.1169 e
|--------------------------------------------------
Residual |                 6
-----------+--------------------------------------------------
Total |                 7
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on 
The between-subjects factor is not significant. Next, we code the contrasts among the dependent variables and test for the a*y interaction (between-subject*within-subjects) interaction.
mat ymat = (1,0,0,-1\0,1,0,-1\0,0,1,-1)
mat list ymat

ymat[3,4]
c1  c2  c3  c4
r1   1   0   0  -1
r2   0   1   0  -1
r3   0   0   1  -1

/* test of the a*y interaction */

manovatest a, ytransform(ymat)

Transformations of the dependent variables
(1)    y1 - y4
(2)    y2 - y4
(3)    y3 - y4

W = Wilks' lambda      L = Lawley-Hotelling trace
P = Pillai's trace     R = Roy's largest root

Source |  Statistic     df   F(df1,    df2) =   F   Prob>F
-----------+--------------------------------------------------
a | W   0.1443      1     3.0     4.0     7.91 0.0371 e
| P   0.8557            3.0     4.0     7.91 0.0371 e
| L   5.9296            3.0     4.0     7.91 0.0371 e
| R   5.9296            3.0     4.0     7.91 0.0371 e
|--------------------------------------------------
Residual |                 6
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F
Even though the interaction is significant, we will go ahead and test the effect of the within-subjects variable. To do this we will create a contrast for the predictor variables, such that, the levels of each variable sums to one.
/* test of y */

mat xmat = (1, .5, .5)
mat list xmat

xmat[1,3]
c1  c2  c3
r1   1  .5  .5

manovatest, test(xmat) ytransform(ymat)

Transformations of the dependent variables
(1)    y1 - y4
(2)    y2 - y4
(3)    y3 - y4

Test constraint
(1)    _cons + .5 a[1] + .5 a[2] = 0

W = Wilks' lambda      L = Lawley-Hotelling trace
P = Pillai's trace     R = Roy's largest root

Source |  Statistic     df   F(df1,    df2) =   F   Prob>F
-----------+--------------------------------------------------
manovatest | W   0.0275      1     3.0     4.0    47.19 0.0014 e
| P   0.9725            3.0     4.0    47.19 0.0014 e
| L  35.3944            3.0     4.0    47.19 0.0014 e
| R  35.3944            3.0     4.0    47.19 0.0014 e
|--------------------------------------------------
Residual |                 6
-------------------------------------------------------------
The test of the within-subjects factor is also significant, although care must be taken in interpreting this result due to the significant interaction effect.

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