Tag Archives: Entropy

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",
+ head=TRUE,sep=";")
> library(rpart)
> cart<-rpart(PRONO~.,data=MYOCARDE)

we get

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

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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. https://latex.codecogs.com/gif.latex?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 https://latex.codecogs.com/gif.latex?\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

  C <- abc2xy(matrix(p,1,3))
  C1 <- abc2xy(matrix(p1,1,3))
  C2 <- abc2xy(matrix(p2,1,3))
  C3 <- abc2xy(matrix(p3,1,3))

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


For a case where there is inequality, use for instance


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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…