Adding between subject factor reduces p value of main effect? I'm investigating the effect of tumor location on mood (depression / anxiety) and also seeing if time has an effect at two intervals (t0 and t1).
I had a data set with Time as a repeated measurement variable, Horizontal location of tumor as an independent variable (categorical) and Mood score as a dependent variable. In my first analysis Time turned out to be significant so I thought great, I may have got something here. Horizontal location was not significant (i.e., regardless of horizontal location of the tumor time still had an effect).
Next, I added another between-subject variable, namely Vertical location of tumor, to the analysis. However, if I now run this three-way factorial repeated measure design time doesn't turn out to be a significant factor on mood anymore! I feel this is weird because it was significant in a two way and now it isn't in a three way? (Horizontal location and vertical location both don't turn out significant.)
So my question boils down to: how come that adding an additional between factor variable makes the main effect of time turn non-significant (increases the p-value)?
Am I allowed to run two two-way interaction with Horizontal / Vertical location separated instead of one big three-way or does that confound the results? 
 A: There are many possible solutions. Unfortunately the best solution in my opinion has more to do with the approach to data analysis. I don't take much stock in these kinds of exploratory analyses. It seems you have fit a lot of models and did not a priori settle upon the correct model for the question. Or, if you did, I would report those findings and note the results of the secondary analyses with careful deliberation that the results are highly prone to detect spurious associations.
Lack of association in these cases is almost always a precision issue. I'm assuming the design was balanced, so study time is by design independent of any of the baseline tumor values. 
In that case, I would mention the following if it is consistent with the line or reasoning: in repeated measurement models for subjective outcomes, there is a chance that growth effects are present. Here mood has a tendency to elevate / worsen as a function of duration of study participation. However we also note veticle tumor location models estimated noted effects, but together there was not sufficient precision to detect both effects in the same model. 
