# Spliting a Node in a Tree

If we grow a tree with standard functions in R, on the same dataset used to introduce classification tree in some previous post,

> MYOCARDE=read.table(
+ "http://freakonometrics.free.fr/saporta.csv",
> library(rpart)
> cart<-rpart(PRONO~.,data=MYOCARDE)

we get

> library(rpart.plot)
> library(rattle)
> prp(cart,type=2,extra=1)

# Visualizing Inequalities in a 3-Person Economy

Yesterday, in the course on inequalities, I mentioned (too) briefly the 3-person Economy. I wanted to spend some time in a short post on visualisations of inequalities in such a context. As mentioned in the slides,  it is possible to use a ternary plot representation. In the case where we believe that the scale independence principle makes sense, i.e. $I(\lambda\boldsymbol{x})=I(\boldsymbol{x})$. A distribution of incomes can be represented as a barycenter in an equilateral triangle (also called de Finetti diagram). The midpoint is the equal situation: the three agents share the same wealth. Because of the scale independence property, we can look at distribution of wealth on the simplex. A wealth distribution is a vector $\boldsymbol{\omega}=(\omega_A,\omega_B,\omega_C)$ where each component is one of the (red) distance below. A is on top of the triangle, and the vertical distance is proportional to the wealth of A. The closer to the bottom line, the poorer A is.

To visualize this distribution of wealth, we can use the trifield package. To add the point and the three segments, the code is

tripoint=function(s){
p=s/sum(s)
p1=c(0,s[2]+s[1]/2,s[3]+s[1]/2)/sum(s)
p2=c(s[1]+s[2]/2,0,s[3]+s[2]/2)/sum(s)
p3=c(s[1]+s[3]/2,s[2]+s[3]/2,0)/sum(s)
C <- abc2xy(matrix(p,1,3))
points(C,pch=19,col="red",cex=2)
C1 <- abc2xy(matrix(p1,1,3))
C2 <- abc2xy(matrix(p2,1,3))
C3 <- abc2xy(matrix(p3,1,3))
segments(C1[1],C1[2],C[1],C[2],lwd=2,col="red")
segments(C2[1],C2[2],C[1],C[2],lwd=2,col="red")
segments(C3[1],C3[2],C[1],C[2],lwd=2,col="red")
}

For instance, to visualize the equal case (inequality indices are defined as a distance to this situation)

tripoint(c(1,1,1))

For a case where there is inequality, use for instance

tripoint(c(1,2,3))

# Inequalities, course 3

Tomorrow, we will discuss inequality indices, from a statistical perspective, and also an axiomatic point of view. In order to illustrate, we will use to following dataset,

> income <- read.csv("http://www.vcharite.univ-mrs.fr/pp/lubrano/cours/fes96.csv",sep=";",header=FALSE)\$V1

Slides can be found online. Since it is the first year I give this course, all comments are welcome…