re: st: Re: ancova for repeated designs

[David Airey <david.airey@vanderbilt.edu>]

Ammending my comments after Joseph Coveney's comments:

. clear

. 
. set obs 30
obs was 0, now 30

. 
. egen id = seq(), from(1) to(10) block(3)

. egen t = seq(), from(1) to(3) block(1)

. egen g = seq(), from(1) to(3) block(3)

. 
. gen y = invnorm(uniform())

. 
. sort id t

. bysort id: gen x = y[1]

. 
. list in 1/9, sep(3)

+------------------------------------+
| id   t   g           y           x |
|------------------------------------|
1. |  1   1   1   -.2711983   -.2711983 |
2. |  1   2   1    1.305697   -.2711983 |
3. |  1   3   1   -.9267018   -.2711983 |
|------------------------------------|
4. |  2   1   2    1.007973    1.007973 |
5. |  2   2   2    .1002743    1.007973 |
6. |  2   3   2   -.4517168    1.007973 |
|------------------------------------|
7. |  3   1   3     1.33716     1.33716 |
8. |  3   2   3   -.2607474     1.33716 |
9. |  3   3   3    1.758486     1.33716 |
+------------------------------------+

. 
. anova y g / id|g x x*g t g*t if t > 1, repeated(t) continuous(x)

Number of obs =      20     R-squared     =  0.4821
Root MSE      = .906211     Adj R-squared = -0.4058

Source |  Partial SS    df       MS           F     Prob > F

-----------+----------------------------------------------------
Model |  5.35051558    12  .445876298       0.54     0.8317
|
g |  .354589496     2  .177294748       0.31     0.7500
id|g |  2.29205779     4  .573014447   

-----------+----------------------------------------------------
x |  .832198807     1  .832198807       1.01     0.3476
x*g |   .20357273     2  .101786365       0.12     0.8853
t |   .13150485     1   .13150485       0.16     0.7010
g*t |  .869877597     2  .434938799       0.53     0.6107
|
Residual |  5.74852951     7  .821218502   

-----------+----------------------------------------------------
Total |  11.0990451    19  .584160268   


Between-subjects error term:  id|g
Levels:  10        (4 df)
Lowest b.s.e. variable:  id
Covariance pooled over:  g         (for repeated variable)

Repeated variable: t
Huynh-Feldt epsilon        =  2.6667
*Huynh-Feldt epsilon reset to 1.0000
Greenhouse-Geisser epsilon =  1.0000
Box's conservative epsilon =  1.0000

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box

-----------+----------------------------------------------------
t |      1     0.16   0.7010   0.7010   0.7010   0.7010
g*t |      2     0.53   0.6107   0.6107   0.6107   0.6107
Residual |      7

-----------+----------------------------------------------------

. 
. adjust x if id<=4, by(g t id)

--------------------------------------------------------------------------------
Dependent variable: y     Command: anova
Covariate set to mean: x = .36113495
--------------------------------------------------------------------------------

------------------------------------------------------------------------
|                           id and t                          
| ------------- 1 ------------    ------------- 2 ------------
g |        1         2         3           1         2         3
----------+-------------------------------------------------------------
1 |           -.135936  -.135706                                
2 |                                            .740559   .470278
3 |                                                             
------------------------------------------------------------------------

------------------------------------------------------------------------
|                           id and t                          
| ------------- 3 ------------    ------------- 4 ------------
g |        1         2         3           1         2         3
----------+-------------------------------------------------------------
1 |                                           -.252478  -.252248
2 |                                                             
3 |            .562489   1.32355                                
------------------------------------------------------------------------
Key:  Linear Prediction

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end of do-file

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