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.

clear
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,  we will create k-1 contrasts. These contrasts are created in a manner similar to that which is done with categorical predictors. We will create the contrasts using effect coding.

mat ycomp = (1,0,0,-1,1,0,-1,0,1,-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.

clear
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,-1,1,0,-1,0,1,-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.