Ozone graphical models

Ozone - max concentration

Ozone = read.table("https://perso.univ-rennes1.fr/valerie.monbet/MachineLearning/Ozone.dat",header=TRUE,row.names=1)
pairs(Ozone[,c(1,3,6,9,11)], panel = panel.smooth, main = "Ozone",pch=20)

Gaussian graphical models

First fit a graphical model on a subset of the variables. The regularizaiton constant is chosen to be equal to 0.5. You can try to change it.

require(glasso)

## Loading required package: glasso

require(qgraph)

## Loading required package: qgraph

require(fields)

## Loading required package: fields

## Loading required package: spam

## Loading required package: dotCall64

## Loading required package: grid

## Spam version 2.1-1 (2017-07-02) is loaded.
## Type 'help( Spam)' or 'demo( spam)' for a short introduction 
## and overview of this package.
## Help for individual functions is also obtained by adding the
## suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

## 
## Attaching package: 'spam'

## The following objects are masked from 'package:base':
## 
##     backsolve, forwardsolve

## Loading required package: maps

C.ozone = cor(Ozone[,c(1,3,6,9)])
a = glasso(C.ozone,.5) # 
qgraph(a, layout="spring",
       labels=names(Ozone[,c(1,3,6,9)]), label.scale=FALSE,
       label.cex=1, node.width=1)

The precision matrix should show the same structure

image(1:nrow(a$wi),1:ncol(a$wi),a$wi[nrow(a$wi):1,],xlab="",ylab="",axes=FALSE,col=tim.colors(64))
box()
axis(2,1:nrow(a$wi),labels = colnames(C.ozone),las=2)
zer = which(a$wi[nrow(a$wi):1,]==0,arr=TRUE)
points(zer,pch=4,cex=2)