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Orthogonal vs. Non-orthogonal contrasts

Dear Yasu,

The contrast x = c(1, -1, 0) is equivalent to beta_x * 1 * a_1 + beta_x *
(-1) * a_2 + beta_x * 0 * a_3.
Likewise contrast y = c(.5, -.5, 0) is equivalent to beta_y * 0.5 * a_1 +
beta_y * (-0.5) * a_2 + beta_y * 0 * a_3.

Since both model the same thing beta_x * 1 * a_1 + beta_x * (-1) * a_2 +
beta_x * 0 * a_3 = beta_y * 0.5 * a_1 + beta_y * (-0.5) * a_2 + beta_y * 0
* a_3.
Some simple math will show that beta_x = 2 * beta_y

Your contrasts are correct but pointless given your model. They are only
meaningful in case FactorA is only a main effect. You included FactorA in
some interactions as well. So you'll need to define contrasts on the full
set of fixed parameters to get some sensible results. You can do that with
the multcomp package. I would also suggest that you find some local
statistician to help you define the contrasts relevant for your model.

Best regards,


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2016-05-26 6:31 GMT+02:00 Yasuaki SHINOHARA <y.shinohara at aoni.waseda.jp>: