Generalized linear model (GLM) question
[DATA]
- Response variable.
- Predictor 1 (is a LINEAR positive correlate of response variable).
- Predictor 2 (is a NON-LINEAR negative correlate of response variable).
[WORRY]
With generalized linear model (Gaussian, Identity), as I understand it, the response variable is played with to make it be a linear function of the predictors. But can this be done in this case where the two predictors have such different relations to the response variable? Maybe it can only manage to get to linearity for one of the predictors, probably the one that is already a linear function of response variable, which is then reported as significant, and the other is "thrown away" (low significance reported)? I think this is what is happening in this case. But is this actually correct, or reflects a limitation of the method? Might an actual non-linear regression come to a different result (with that non-linear variable not thrown away)?
N.B. Extra information which might help, or might not help, forum answer: Predictor 2 can be made a LINEAR correlate of Response variable by logging Predictor 2.
Comments
imo, it starts by a model for the data-generating process (Normal? Poisson?). Then the model parameter of interest is modeled as a linear combination of predictors, possibly on thea suitable scale. Any nonlinear effects on this scale can possibly be handled by appropriate transformations. See https://towardsdatascience.com/generalized-linear-models-9cbf848bb8ab
Cheers,
EJ