Regression - Is it incorrect to *not* include an independent variable I'm not interested in, but which *may* affect the depend variable? I am conducting an ordinal logistic regression. I have an ordinal variable, let's call it Change, that expresses the change in a biological parameter between two time points 5 years apart. Its values are 0 (no change), 1 (small change), 2 (large change).
I have several other variables (VarA, VarB, VarC, VarD) measured between the two time points. My intention is to perform an ordinal logistic regression to assess whether the entity of Change is more strongly associated with VarA or VarB. I'm really interested only in VarA and VarB, and I'm not trying to create a model. VarC and VarD are variables that I know may affect Change, but probably not very much, and in any case I'm not interested in them. I just want to know if the association in the period of observation (5 years) was stroger for VarA or for VarB.
Would it be wrong to not include VarC and VarD in the regression?
 A: This depends on the relationships between the predictor variables (how are VarC and VarD related to VarA and VarB?) and also what question you are trying to answer.
Consider the possible case where VarA causes VarC which causes the response.  If your only interest is the relationship between VarA and the response then including VarC would hide the indirect relationship.  But if we are interested in if VarA has a direct effect on the response above and beyond the indirect effect through VarC then including VarC is important.
Sometimes it is helpful to draw a diagram with all the different variables and then draw lines/arrows showing the potential and/or interesting relationships between all the variables.  Then use that along with the question of interest to decide on the model.
A: I suppose it is best to show one model,the original model, that includes them. Including any possible interactions.Than you may reason, based on your findings, whether they can be removed due to their statistical properties (no significance, causing non normal errors, variance inflation, etc.) or domain specific factors (e.g., HP may be significant if you try to forecast how much a car is desired but may not be adequate in a study on color preferences of car vendors). The result would be a model that is suitable to the domain and statistically relevant.
