## Least square approximation. This version Oct 19, 2006
## Reference Wang, H. and Leng, C. (2007)
##
## Written by Hansheng Wang
## Comments and suggestions are welcome
##
## README: lsa() takes the fitted oject (e.g., from lm(),
## 	glm(), coxph(), rq(), etc) as its only input and  
## 	find the optimal estimator according to AIC or BIC.
##	In order to make lsa() useful, the corresponding
##	R object should at least implement coef() and vcov()
##	functionalities. lsa() uses this to extract the 
##	coefficients and its covariance matrix estimate.


source("LSA.R")							#load the LSA code

#LSA with linear model
	library(lars)						#load the lars package
	data(diabetes)						#load the diabetes data
	lm.obj=lm(y~x,data=diabetes)				#fit linear model
	lsa.obj=lsa(lm.obj)					#find LSA estimator

#LSA with logistic regression
	library(glmpath)					#load glmpath package
	data(heart.data)					#load the heart data
	glm.obj=glm(y~x, family=binomial,data=heart.data)	#fit logistic regression
	lsa.obj=lsa(glm.obj)					#find LSA estimator
 
#LSA with Cox's model
	library(survival)					#load survival library
	data(lung)						#load lung data
	lung$status=lung$status-1				#create censor indicator
	lung$sex=lung$sex-1					#creat gender dummy
	cox.obj=coxph(Surv(time,status)~age+sex+ph.ecog+ph.karno+pat.karno+meal.cal+wt.loss,data=lung)
	lsa.obj=lsa(cox.obj)					#find LSA estimator

#LSA with AFT model
	library(survival)					#load survival library
	data(lung)						#load lung data
	lung$status=lung$status-1				#create censor indicator
	lung$sex=lung$sex-1					#creat gender dummy
	acf.obj=survreg(Surv(time,status)~age+sex+ph.ecog+ph.karno+pat.karno+meal.cal+wt.loss,data=lung,dist="weibull",scale=1)
	lsa.obj=lsa(acf.obj)					#find LSA estimator

#LSA with LAD regression
	library(quantreg)					#load quantreg package 
	x=matrix(rnorm(5000),500,10)				#simulate the X
	y=x[,1]+x[,2]+x[,3]+rcauchy(500)			#simulate the Y
	rq.obj=rq(y~x)						#fit a LAD regression
	lsa.obj=lsa(rq.obj)					#find LSA estimator