#######################################################################################
## Exemplo nlsmsn
#######################################################################################

library(nlsmsn)

##Load the data
data(Oil)

##Define non linear function
nlf<-function(x,betas){
resp<- betas[1]/(1 +betas[2]*exp(-betas[3]*x))
return(resp)
}

##Set the response y and covariate x
y <- Oil$y
x <- Oil$x

## See relationship between y and x
plot(x,y)

##Set initial values
betas <- c(37,4.81,0.78)
sigma2 <- 2.95
shape <- -2
nu <- 3

## Skew.normal regression
analysis.n <- smsn.nl(y=y, x=x, betas=betas, sigma2=sigma2, 
                       shape = shape, nlf = nlf, criteria = TRUE, 
                       family = "Normal", iter.max = 200)

## Skew.normal regression
analysis.sn <- smsn.nl(y=y, x=x, betas=betas, sigma2=sigma2, 
                       shape = shape, nlf = nlf, criteria = TRUE, 
                       family = "Skew.normal", iter.max = 200)

## Skew.t regression
analysis.st <- smsn.nl(y=y, x=x, betas=betas, sigma2=sigma2, shape = shape, 
                       nu = nu, nlf = nlf, criteria = TRUE, 
                       family = "Skew.t", iter.max = 200)

analysis.n$AIC
analysis.sn$AIC
analysis.st$AIC

#######################################################################################
## Exemplo car
#######################################################################################
library(car)
 
data(DNase)

DNase <- subset(DNase, Run == 1)

        
plot(DNase$conc,DNase$density)

plot(log(DNase$conc),DNase$density)

## fit a representative run
fm1 <- nls(density ~ SSlogis( log(conc), Asym, xmid, scal ),
         data = DNase, subset = Run == 1)

## compare with a four-parameter logistic
fm2 <- nls(density ~ SSfpl( log(conc), A, B, xmid, scal ),
         data = DNase, subset = Run == 1)
summary(fm2)
anova(fm1, fm2)

#######################################################################################
## Compare car x nlsmsn
#######################################################################################
data(Oil)

##Define non linear function
nlf<-function(x,betas){
resp<- betas[1]/(1 +betas[2]*exp(-betas[3]*x))
return(resp)
}

##Set the response y and covariate x
y <- Oil$y
x <- Oil$x

## See relationship between y and x
plot(x,y)

##Set initial values
betas <- c(37,4.81,0.78)
sigma2 <- 2.95
shape <- -2
nu <- 3

## Skew.normal regression
analysis.n <- smsn.nl(y=y, x=x, betas=betas, sigma2=sigma2, 
                       shape = shape, nlf = nlf, criteria = TRUE, 
                       family = "Normal", iter.max = 200)

##Define non linear function
nlf2<-function(x,beta1,beta2,beta3){
resp<- beta1/(1 +beta2*exp(-beta3*x))
return(resp)
}

analysis.nl <- nls(y ~ nlf2(x,beta1,beta2,beta3), data = Oil, 
                  start = list(beta1=37,beta2=4.81,beta3=0.78))

coef(analysis.nl)

analysis.n$betas