Re: st: syntax for nested two-factor ANOVA

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

I admit remaining confused about the design and think I may have sent  
you down the wrong path. It is hard to suggest over the listserv,  
without much thought, and without seeing the data.

In looking at the data I see you have replication in the table cells,  
e.g., you have 4 cases for brand 7 and company 1 with a 0 keep  
status. This is making the repeated measures request fail (I think).  
I also see that you sometimes have a company with only one brand for  
sale, so there is no variance in those cases that is separate between  
company and brand.

Also I now imagine the experiment as you obtaining a continuous DV  
measure on each box of cereal that was sold or discarded, and that  
you have more than one box measured per brand, cereal combination.

/*

use http://www.ats.ucla.edu/stat/stata/examples/kirk/spf2-4, clear

// I remembered this example and made a suggestion, not really  
understanding what you were doing

anova y a / s|a b a*b /, repeated(b) // a is between subject, b is  
within subject, a and b are fixed, s is random

anova y a / s|a b / a*b /, repeated(b) // here, a is fixed, b and s  
are random

// both compute without issue and I think are correct when making the  
second factor b random

// looking at some of the data

list in 1/9

     +----------------+
     | a   b   s    y |
     |----------------|
  1. | 1   1   1    3 |
  2. | 1   2   1    4 |
  3. | 1   3   1    7 |
  4. | 1   4   1    7 |
     |----------------|
  5. | 1   1   2    6 |
  6. | 1   2   2    5 |
  7. | 1   3   2    8 |
  8. | 1   4   2    8 |
     |----------------|
  9. | 1   1   3    3 |

// you see the explicit subject factor listed above
*/

You said you had data like (and I made the comparison):

(s)   (a)     (b)  (y)
brand company keep testresult
1 1 1 .839
1 1 0 .605
2 1 1 .798
2 1 0 .567
3 2 1 .855
3 2 0 .650
etc etc etc etc

but you really have data like:

     +------------------------------------+
     |         y   keep   brand   company |
     |------------------------------------|
  1. | -.0800775      0       7         1 |
  2. |   .071272      0       7         1 |
  3. |  .1124799      0       7         1 |
  4. |  .3309362      0       7         1 |
  5. |  .0646274      1       7         1 |
  6. |  .1491636      1       7         1 |
  7. |  .3802552      1       7         1 |
  8. |  .3819582      1       7         1 |
  9. |  .4677568      1       7         1 |

which is really like:

     +------------------------------------------+
     |         y   keep   brand   company   box |
     |------------------------------------------|
  1. | -.0800775      0       7         1     1 |
  2. |   .071272      0       7         1     2 |
  3. |  .1124799      0       7         1     3 |
  4. |  .3309362      0       7         1     4 |
  5. |  .0646274      1       7         1     5 |
  6. |  .1491636      1       7         1     6 |
  7. |  .3802552      1       7         1     7 |
  8. |  .3819582      1       7         1     8 |
  9. |  .4677568      1       7         1     9 |


where we have a three factor nested design, with brand nested in  
company and crossed with keep, and keep is between subjects.

Since you don't have brand separable from company for half your  
companies, why not simplify and just control for brand, in which case  
you have a two factor ANOVA with unequal replication with one of your  
factors a random (blocking) effect. Usually you don't interact that  
blocking effect, so:

anova y brand keep

gives the test to look at for keep:

. anova y brand keep

                           Number of obs =      89     R-squared      
=  0.3444
                           Root MSE      = .199951     Adj R-squared  
=  0.2409

                  Source |  Partial SS    df       MS            
F     Prob > F
              ----------- 
+----------------------------------------------------
                   Model |  1.59643837    12  .133036531        
3.33     0.0007
                         |
                   brand |  .504996573    11  .045908779        
1.15     0.3373
                    keep |  .905309904     1  .905309904       
22.64     0.0000
                         |
                Residual |  3.03851904    76  .039980514
              ----------- 
+----------------------------------------------------
                   Total |  4.63495741    88  .052669971


In the case for a two factor ANOVA with one random factor, you might  
allow interactions (unlike the randomized block model above that  
assumes no interactions).

Say A is fixed and B is random, then the test for A is MSA/MSAB, for  
B is MSB/MSE, and for MSAB/MSE.

So you can try also, if you allow interactions,

quietly anova y brand keep / brand*keep /


                           Number of obs =      89     R-squared      
=  0.3971
                           Root MSE      = .204223     Adj R-squared  
=  0.2081

                  Source |  Partial SS    df       MS            
F     Prob > F
              ----------- 
+----------------------------------------------------
                   Model |  1.84058059    21  .087646695        
2.10     0.0116
                         |
                   brand |  .361996382    11  .032908762        
1.21     0.3921
                    keep |  .595857339     1  .595857339       
21.97     0.0011
              brand*keep |  .244142211     9  .027126912
              ----------- 
+----------------------------------------------------
              brand*keep |  .244142211     9  .027126912        
0.65     0.7500
                         |
                Residual |  2.79437683    67  .041707117
              ----------- 
+----------------------------------------------------
                   Total |  4.63495741    88  .052669971


-Dave

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