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I have a model with two categorical variables. Each one has three levels. Iv1 has a natural reference category so I would like to use dummy coding, and compare level 2 to level 1, and level 3 to level 1. Iv2 is sequential and I would like to compare level 2 to level 1, and level 3 to level 2.

R automatically creates contrasts that then look like this:

For Iv1:

  i ii
1 0  0
2 1  0
3 0  1

For Iv2:

         i        ii
1 -0.6666667 -0.3333333
2  0.3333333 -0.3333333
3  0.3333333  0.6666667

Is there anything wrong with using these two kinds of contrasts, and including an interaction between them?

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No problem with these two kinds of coding. For lv1, it is clear the coefficient for i is the effect of level 2 vs level 1 and the coefficient for ii is the effect of level 3 vs level 1. If you want the comparison between level 2 and 3, then use the difference of two coefficient.

For lv2, the coefficient for i is the effect of level 2 vs level 1 and the coefficient for ii is the effect of level 3 vs level 2. If you want the comparison between level 1 and 3, then use the difference of two coefficient.

If the interaction is included in the model, there will be 9 regression coefficients in the model. It equals the number of cells in your design (3 levels in lv1 times 3 levels in lv2 = 9 cells). Then if you want to compare any pair of cells, just plug in the code for each cell and get the difference between them.

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