RuleFit & quantreg: partial dependence plots; showing an effect
They are entirely different: Rulefit is a fiendishly clever combination of decision tree formulation of models and L1-regularization intended to select parsimonious fits to very complicated responses yielding e.g. piecewise constant functions. Rulefit estimates the conditional mean of the response over the covariate space, but permits a very flexible, but linear in parameters specifications of the covariate effects on the conditional mean. The quantile regression plotting you refer to adopts a fixed, linear specification for conditional quantile functions and given that specification depicts how the covariates influence the various conditional quantiles of the response. Thus, roughly speaking, Rulefit is focused on flexibility in the x-space, maintaining the classical conditional mean objective; while QR is trying to be more flexible in the y-direction, and maintaining a fixed, linear in parameters specification for the covariate effects at each quantile. url: www.econ.uiuc.edu/~roger Roger Koenker email rkoenker at uiuc.edu Department of Economics vox: 217-333-4558 University of Illinois fax: 217-244-6678 Champaign, IL 61820
On Dec 20, 2006, at 4:17 AM, Mark Difford wrote:
Dear List, I would greatly appreciate help on the following matter: The RuleFit program of Professor Friedman uses partial dependence plots to explore the effect of an explanatory variable on the response variable, after accounting for the average effects of the other variables. The plot method [plot(summary(rq(y ~ x1 + x2, t=seq(.1,.9,.05))))] of Professor Koenker's quantreg program appears to do the same thing. Question: Is there a difference between these two types of plot in the manner in which they depict the relationship between explanatory variables and the response variable ? Thank you inav for your help. Regards, Mark Difford. ------------------------------------------------------------- Mark Difford Ph.D. candidate, Botany Department, Nelson Mandela Metropolitan University, Port Elizabeth, SA.
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