Repeated measures factorial ANOVA - independent variables from an equation I have responses from 30 patients for 4 independent variables. ind_var1 has 2 levels, ind_var2 has 3 levels, ind_var3 has 2 levels and ind_var4 has 4 levels. No groups in the dependent variable. So the matrix for independent variables is 2X3X2X4. Each patient is measured for all the combinations. So I chose the repeated measures factorial ANOVA design and post hoc tests by choosing preferred combinations of independent variables. But ind_var3 and ind_var4 are related through a mathematical equation. Does this violates using factorial ANOVA model. Also, I would like to whether my choice of test is appropriate according to the variable properties I described. Thank you in advance!

Relations between the independent variables are not relevant for ANOVA. And the formula you gave in the comments looks like those two variables only appear in the same equation but don't determine each other's values. Thus this doesn't prevent you from going through all combinations. Thus, no, this doesn't violate any assumptions for factorial ANOVA.
And everything you describe seems coherent, so, based on the information given, the choice of your tests is appropriate. Just make sure that you provide for all the assumptions required by ANOVA and your post hoc test.
