if( !require('investr') ){
    install.packages('investr', dependencies=TRUE, repos='http://cran.rstudio.com/')
}
library(investr) # has the function plotFit

library(MASS)
data(wtloss)

plot(wtloss$Days, wtloss$Weight, xlab='Days', ylab='Weight')
grid()

# Build a self-starter function for this model:
#
shiftedExpModel = function(predictor, b, y0, c){
    y0 * exp(predictor/b) + c
}

shiftedExpModelInit = function(mCall, LHS, data){
    xy = sortedXyData(mCall[['predictor']], LHS, data)
    n = dim(xy)[1]
    c = xy[n,'y'] - 1 # this makes y - c = 1 when y is the last (sorted according to x) value
    xy[,'y'] = xy[,'y']- c
    lmFit = lm(log(xy[,'y']) ~ xy[,'x'])
    coefs = coef(lmFit)
    y0 = exp(coefs[1])
    b = 1/coefs[2]
    value = c(b, y0, c)
    names(value) = mCall[c('b','y0','c')]
    value
}

shiftedExpModelSS = selfStart(shiftedExpModel, shiftedExpModelInit, c('b','y0','c'))

# Fit our model to the given data:
#
wtloss.m1 = nls(Weight ~ shiftedExpModelSS(Days, b, y0, c), data=wtloss, trace=FALSE)
print(summary(wtloss.m1))

#postscript("../../WriteUp/Graphics/Chapter3/chap_3_prob_3.eps", onefile=FALSE, horizontal=FALSE)
plotFit(wtloss.m1, main='wtloss data and fit')
grid()
#dev.off()