Should I include IVs in my Regression model if my DV is based on them? I'm doing a linear regression model where I test whether certain factors influence how (in)consistent people are between what they say ("attitudes") and what they do.
Question in Short: I have two variables of which I calculate percentile rankings, then substract these from another, and use this end result as my DV. Should I include the original variables (not the percentile rankings) in my regression model?
Details
My dependent variable is a proxy for inconsistency:

*

*calculate percentile rank of individual on the attitudes scale (Likert 1-7) compared to sample: higher percentiles mean the individual has more favourable attitudes towards the concept of my study. E.g. respondent X is at 90th percentile meaning they have favourable attitudes compared to the rest of the sample.

*calculate percentile rank of individual on the behaviour scale: higher percentiles mean the individual seeks out more information towards the concept of my study.

*Substract 2 from 1: E.g. respondent X is 90th percentile for attitude and 40th percentile for behaviour --> 0.9 - 0.4 = 0.5

In my model then, is it acceptable/necessary to include the variables from 1. and 2. in the regression model as independent variables?
I have done this and both variables are significant. The attitudes variable is positive meaning that people with more favourable attitudes are generally more inconsistent compared to the rest of the sample.
 A: The percentile ranks for each variable mean approximately the same thing as the original variables; they carry almost the same information. If all of the 7 categories are used for each measure and you gives ties for equal scores, the percentiles ranks carry exactly the same information as the original variables, just rescaled to be between 0 and 100 instead of between 1 and 7.
With this understanding that the original variable and the percentile rank are interchangeable, ask whether it makes sense to regress your outcome on the predictors. That is, what will running the following regression tell you?
$$
r(A_i)-r(B_i) = \beta_0 + \beta_1 r(A_i) + \beta_2 r(B_i) + \varepsilon_i
$$
(Here, $r(X)$ means the percentile rank transformation of $X$.) It should be clear that by necessity, $\beta_0 = 0$, $\beta_1 = 1$, $\beta_2 = -1$, and $\text{Var}(\varepsilon) \equiv\sigma_\varepsilon^2=0$. This regression will tell you nothing except the formula you used to calculate the outcome. Of course the predictors will be significant; they jointly explain ALL the variance in the outcome. Using the original variables will give you the same result, but with the coefficients on a different scale. That still doesn't tell you anything about the world.
Running univarible regressions might tell you something more, i.e., if you regress the consistency score on just the behavior scale, then you might be able to say something about the relationship between behavior and consistency. A problem, though, is that this essential boils down to just asking about the relationship between behavior and attitudes and doesn't really tell you much about consistency. For example, let's say you fit the model
$$
r(A_i)-r(B_i) = \beta_0 + \beta_1 r(B_i) + \varepsilon_i
$$
If you add $r(B_i)$ to both sides, that's exactly the same thing as fitting the model
$$
r(A_i) = \beta_0 + \beta_1^* r(B_i) + \varepsilon_i
$$
where $\beta_1^* = \beta_1 + 1$. So you're just back to finding the relationship between behavior and attitudes. That may be interesting, and, indeed, the correlation between those variables should be informative for your study. But asking whether there is a relationship between consistency and behavior is exactly the same thing (i.e., has the same statistical meaning) as asking whether there is a relationship between attitudes and behavior.
