# March 26, 2009    Generalized Additive Models


library("mgcv")	    	# to get gam program
library("MASS")		# to get dataset  birthwt

	low   - birth wt less than 2.5 kg
	age   - mother's age
	lwt   - mother's weight (lbs)
	race  - white/black/other
	smoke - yes/no
	ptl   - number of previous premature labors
	ht    - history of hypertension
	ui    - uterine irritabiliy
	ftv   - number of MD visits in first trimester
	bwt   - birth wt (grms)


b = gam( low ~ s(age), data=birthwt)

attach(birthwt)

race = factor( race, labels=c("white","black","other"))

table(ptl)     # 159 24 5 1    compress to  =0   >0
ptd = factor( ptl>0 )

table(ftv)    #  100  47  30   7   4   0  1    compress to 0 1 >=2
ftv = factor(ftv); levels(ftv)[-(1:2)] = "2+"

bwt = data.frame( low=factor(low), age, lwt, race,
      		  smoke = (smoke>0), ptd, ht = (ht>0),
		  ui = (ui>0), ftv )
detach(); rm(race,ptd,ftv)



#######  logistic regression (full)  ########

birthwt.glm = glm( low ~ ., family=binomial, data=bwt )
summary(birthwt.glm)
plot(birthwt.glm)

table( bwt$low, predict(birthwt.glm)>0 )

       ##    FALSE TRUE
       ##  0   116   14
       ##  1    37   22


#########   use GAM to see if linear   #############


attach(bwt)
b = gam( low ~ s(age,k=3,fx=TRUE,bs="cr") + s(lwt,k=5,fx=TRUE,bs="cr") +
    smoke + ptd + ht + ui + ftv, binomial, bwt )
summary(b)
plot(b)

table( bwt$low, predict(b)>0 )
   
       ##    FALSE TRUE
       ##  0   112   18
       ##  1    38   21