I have read a few answers (e.g. this, this and this) recommending to use Ordinal Logistic Regression (OLR) as a generalized method when Kruskal-Wallis is not suitable. For instance, a 2x2 factorial design since K-W is the non-parametric equivalent of one-way ANOVA.
My situation: I have a 2x2 design with two treatment variables and each has two levels (so 4 treatments in total). Each variable represents the level of exposure of subjects to some environmental factor. There are two possible values:
high, and I encode them as
0 (low) and
1 (high) in Stata.
I also have several other variables measuring different characteristics of the subjects after being exposed to different combinations of levels of exposure. I want to explore the individual as well as the interaction effects of the two treatment variables on these characteristics.
I am convinced that I should use OLR to do this, but I have a few questions regarding its implementation:
Is it correct to run one regression per characteristic individually (so each characteristic as the dependent variable)?
These characteristic variables are continuous, so is it appropriate to use them as the dependent variable in a OLR? I guess it is fine, as OLR handles an ordinal variable and a continuous variable is also ordinal?
How do we run the regression exactly? For example, if an interested dependent variable is
a, and the treatment/independent variables are
c, do we simply do
ologit a i.b i.cin the case of Stata? (http://www.ats.ucla.edu/stat/stata/dae/ologit.htm) But then how do we find out about the interaction effect?
When do we include other variables in the regression in addition to the (categorical) treatment variables? For example, independent variables like age, sex, etc.
Do we need to adjust for anything when using OLR this way? I see a few options to use with
ologitin Stata (http://www.stata.com/manuals13/rologit.pdf), but am inexperienced to decide which to use, if any.
Finally, is it possible to achieve pairwise comparison across treatments using OLR? If so, how do we do it in Stata?