I have a dataset which included 3 categorical predictors and continuous variable responding to change in the level of predictor. The effect of each combination of predictors has been measured 30 times. The problem is that distributions of response variable for each combinations of predictors are different by nature, and thus no homogenity of variances nor even some common type of distribution could be suggested.
So, I wonder what kind of analysis could be applied to assess quantitavely the relative effect of predictors on the responces? Thanks in adnvance!
hello Nickolay Markov
you can draw PCA and Violin plot like in this Article Manganese (Mn) removal prediction using extreme gradient model
Good Luck!
Thank you, Suraj, but I'm afraid that PCA doesn't fit to my goal. I really don't want to reduce the number of inependent variables, I need to estimate the effect for each of them.
Hello Nickalay,
Do you mean that you have 30 cases/replications for each possible combination of levels for three independent variables (the categorical variables), and a resultant measured score for each case?
If so, either a 3-way anova or multiple linear regression would allow you to address the influence of the individual IVs ("main effects") and their combinations ("interactions"). If I've misunderstood your design, perhaps you could explain it a bit further.
Good luck with your work.
Hello, David
thank you for your comment
this is exactly what I mean. But the problem with ANOVA is that it suggest the equality (or at least similarity) of variances of the scores in each experiment. In my case the variances are very different. Also, I cannot apply MLR because the number of levels is too low (maximum 5).
The best solution I have now is "by group" Kruskal-Wallis test, but maybe there could be more ambitious decisions?
Maybe one of these methodologies can serve with interpretation tutorial
https://gamlj.github.io/rosetta_moderation.html#gamlj_glm
Also suggest MANOVA
Hello again, Nikolay,
Kruskal-Wallis also presumes homogeneity (though normality is no longer an issue). Why not try bootstrapped error estimates within the anova framework? A number of statistical software packages offer this option.
Permutation/Exact tests would also work, but the computation to enumerate all possible data assortments can become quite daunting as sample size and the number of conditions to be compared increases.
Good luck in finishing your project.
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