Re: ANOVA with empty cells

[Isaac Neuhaus]

Please see bellow.

Mike Miller wrote:

> On Mon, 11 Apr 2005, Isaac Neuhaus wrote:
>
> > How does SAS do it?
> >
> > Source   DF     Type III SS     Mean Square    F Value    Pr > F
> > R         3     36.30000000     12.10000000      48.40    0.0203
> > T         1      4.08333333      4.08333333      16.33    0.0561
> > R*T       1      0.75000000      0.75000000       3.00    0.2254
>
>
>
> You'll have to look at their manuals to figure out what they are 
> doing. Note that you have 3 df for R, 1 df for T, but only one df for 
> R*T.  It must be fitting a model with a sort of partial interaction 
> effect.  In a full model, you would have 3*1 = 3 df for interaction.

Yes.... this is because there are two empty cells in the design, but how 
are they calculating it?

> Looking more closely, you can only fit an interaction to the part of 
> the model where f1 is 1 or 3.  So that must be what it is doing.  You 
> can do this in Octave using dummy codes.  You need three dummy codes 
> for f1, one for f2, and one for (arbitrary choice here) when f1=1, 
> f2=1.  Once you have that done, you can use the '\' operator and other 
> functions to solve this,


That is pretty much what I did but I do not get the same answer although 
it is close. Here is my design matrix:

X = [ 1, 1, 0, 0, 1, 0;
     1, 1, 0, 0,-1, 0;
     1, 1, 0, 0,-1, 0;
     1, 0, 1, 0, 1, 0;
     1, 0, 0, 1, 1, 1;
     1, 0, 0, 1,-1,-1;
     1, 0, 0, 1,-1,-1;
     1,-1,-1,-1,-1, 1]

And here are my contrast matrices and their results (which I believe are 
not approximation errors):

C1 = [0,1,0,0,0,0;
     0,0,1,0,0,0;
     0,0,0,1,0,0]    pval = 0.0178    (in SAS 0.0203)

C2 = [0,0,0,0,1,0]    pval = 0.0550    (in SAS 0.0561)

C3 = [0,0,0,0,0,1]    pval = 0.2254    (the same in SAS)

Isaac

> but I'm sure someone has developed a little regression or ANOVA 
> package to make this easier.
>
> Mike
>
>
> > > Your data....
> > >
> > > >     f1   f2   response
> > > > S1    1    1    7
> > > > S2    2    1    1
> > > > S3    3    1    4
> > > > S4    4    2    5
> > > > S5    3    2    5
> > > > S6    1    2    9
> > > > S7    3    2    5
> > > > S8    1    2    10



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