thanks. Do you have a preference between cubic splines, restricted cubic splines (some call these natural splines), and b splines. I am still unclear if you can interpret the coefficients generated or you just look at the graphs.
I believe historically I used b splines. Interpretation comes down to the purpose of the term. If I am just using it to control for imbalances - an explicit interpretation isn't needed. If the term is the target exposure, then interactions, stratifications, or quantile regression can be used.
"Something else to remember is that the coefficients on a model with natural splines defy any sort of interpretation. So forget using the “1-unit increase in x leads to a __ increase in y” method to explain association. An alternative approach is an effect plot, which allows you to visualize your model given certain predictor values. "
So, ignoring that Jake and Dason and hlsmith know what they are talking about, how does one interpret the impact of a predictor that has a non-linear relationship to Y? Just run the regression at certain levels of X?
First you have to have confidence that the signal is true. Perhaps find it in a random set then get the estimate from the holdout set and make sure the residuals look good. When sub setting it into piece wise regression.
The key thing is to make sure you aren't over fitting the curve. Remember, you CAN get point estimates and predictions from the model GAM, you just don't get a single coefficient, since the relationship isn't linear.