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RE: st: Anova and Contrasts with missing cells


From   "Steichen, Thomas J." <SteichT@RJRT.com>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Anova and Contrasts with missing cells
Date   Mon, 27 Oct 2008 13:30:39 -0400

My thanks to Joseph Coveney and David Airey for replying. I'll use Joseph's comments as a basis for a few more thoughts.

Joe says:

>> Your contrast statement doesn't specify the contrast that
>> you intended.

Clearly this was true if one confines that statement to Stata, however, both SAS and JMP interpreted a highly similar method of specifying the contrast as being what I intended. One can debate whether my intention was a reasonable intention but, assuming it was, Stata tested something else. My question from my first post, "Which is right?", still stands. Maybe a better question is, What do the two contrasts, the one I used and the one Joe proposes, really say? In Stata format, these would be:

lincom _coef[round[3]] - _coef[round[1]]
lincom _coef[round[3]] - _coef[round[1]] + _coef[size[1]] / 2

Or

test _coef[round[1]] = _coef[round[3]]
test _coef[round[1]] = _coef[round[3]]  + _coef[size[1]] / 2

Joe also said:

>> First, I recommend to specify the ANOVA model as
>>    anova nnn round size
>> which in this case happens to be equivalent to
>>   -anova nn round size|round-,
>> but will give a clearer readout of what follows:

And then proceeded to use -lincom- to test the contrast:

>> anova, regress
>> With that in view, in order to get the correct contrast
>> (and the one that SAS and JMP report):
>> lincom _coef[round[3]] - _coef[round[1]] + _coef[size[1]] / 2

Interstingly, Joe use the phrase "correct contrast", but I think he really only meant the contrast that tests what appears to be what I intended.

My actual point in quoting the above revolves around the choice of specifying the model as -anova nnn round size- versus -anova nn round size|round- and the resulting impact on testing. As Joe says, the ANOVA estimates are the same (well, he doesn't say exactly that, but I think that is what he means by "equivalent"), however, it appears there is no way to specify the contrast based on nested model symbolism. That is, I was unable to find a way to symbolicly specify anything about -size|round- using that notation in either -test- or -lincom-. Alternatively, after the nested model (or the crossed model), one can specify:

  test _b[round[1]] =  _b[round[3]] +  _b[size[1]*round[3]] / 2

Or

  mat test13 = (0,    1, 0, -1, 0, 0,   -.5, 0, 0, 0, 0, 0)
  test, test(test13)

And the test will be performed. The first of these clearly resorts to crossed-model notation (even in the nested setup!).

My question: Is there a way to directly specify a nested term in -test- or -lincom- using nested notation (i.e., of the form: a|b)? If there is, I haven't found it.

Joe then mentions Milliken and Johnson:

>> Factorial ANOVA with missing cells is a real bear, and contrasts
>> after it is even worse.  See Chapter 13 in George A. Milliken &
>> Dallas E. Johnson, _Analysis of Messy Data_ Volume 1: Designed
>> Experiments (London: Chapman & Hall, 1992).

I pulled the book off my shelf only to discover that I had (in a prior iteration through a similar problem, likely 10 years ago) highlighted essentially every key point concerning the issues underlying the differences above.

Clearly, in this model, SAS and JMP test a contrast on -round- of the form (1, 0, -1, 0, 0) differently than Stata does. That implicitly implies that the packages assume different things to make it testable. In Stata notation, SAS and JMP test contrast matrix (0,  1,0,-1,0,0,  -.5,0,0,0,0,0) while Stata tests (0,  1,0,-1,0,0,  0,0,0,0,0,0) (i.e., exactly what I specified!). It also implies that the interpretation of those tests depend on those assumptions. I don't know what to say about that other than to be cautious!

Tom



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