I'm running two identical logistic models on two different (and with mutually exclusive 1's) DVs on the same dataset. I have an independent variable with similar coefficient in both models and I wanted to check for the assumption of linearity. Graphically, the relationship between $X_1$ and the log odds of both DVs appear almost identical and rather linear.
I ran the Box–Tidwell for both models to check for linearity. The coefficients of interactions of $X_1$ are almost identical in both, but with opposite sign: positive in the first, negative in the second. In both cases, they are not significant. Moreover, the test for non-linearity (stata, boxtid) has two complete different results:
Coeff/Std. Error: 1.16 (.21) p1= 1.47 Nonlin. dev: 0.249 (P = 0.618) (First Model)
Coeff/Std. Error: 0.74 (.21) p1= -1.03 Nonlin. dev. 9.184 (P = 0.002) (Second Model)
In the first case we cannot reject linearity, as I expected, whereas in the second case the test is significant. I honestly did not get what happened. For sure I expected similar results, since the relationship of the IV appear basically identical with both IVs. Any suggestion? Besides that, should I consider the linearity assumption violated in the second model even if the coefficient of the interaction is non-significant? And why instead the test for non-linearity it is? Thanks in advance.