"Best" Multiple (Multivariate) Nonlinear Regression?

Axl

New Member
#1
Hi all,

I'm just getting started in R. I've had good luck finding the right (predictive) correlation weights using orthogonal polynomials in Java. Where to go from here? Quantile regression was introduced in 1978 and Multivariate Adaptive Regression Splines (MARS) was introduced in 1991. What newer/better methods should I be looking at?

(If it helps I'm trying to find non-linear relationships between 10-12 predictors and 1 response variable. I'd stick with orthogonal equations except that the curse of dimensionality means I'm using only 1st and 2nd order polynomials so there's a good chance the fit is off.)

Thanks,

Axl
 

vinux

Dark Knight
#2
I haven't tried Quantile regression. So no idea.

If you are using simple regression
Using scatter plot and the residual plot , get the idea of the type of non-linear relationship.
Then sometimes the transformation or introducing the polynomial term we can capture the relationship.

There are different types of methods are there.. each one based on different different assumptions..
Eg: Generalized linear model.Generalized additive models or mixed regression. etc
what is the nature of your response variable?
 

Axl

New Member
#3
There are different types of methods are there.. each one based on different different assumptions..
Eg: Generalized linear model.Generalized additive models or mixed regression. etc
what is the nature of your response variable?
Thanks for the response. Good suggestion to use scatter plot and residual plot. I haven't done much visualization.

If I'm understanding the question, all variables are continuous. To make things confusing though, I'm looking for overvalued/undervalued signals in stocks/commodities. So +1 for "buy" and -1 for "sell" could be considered either continuous or categorical (+0.95 - +1.00 means buy... -1.00 - -0.95 means sell... otherwise do nothing).

Will look into GLM (generalized linear model), GAM (generalized additive model), and mixed models aka mixed effects. At first glance GAM looks like a good fit, we'll see...