---
title: "Examples for the corrgram package"
author: "Kevin Wright"
date: "`r Sys.Date()`"
bibliography: corrgram.bib
output:
  html_document:
  theme: cerulean
  highlight: tango
vignette: >
  %\VignetteIndexEntry{Examples for the corrgram package}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
---
<style type="text/css">
body, td { font-size: 14pt; color: #000; padding:1em; }
code, pre, #ws, #message { font-size: 12pt;
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code {border: 1px solid #e0e0e0; padding: 0 5px;}
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## Abstract

The `corrgram` package is an implementation of correlograms.  This
vignette reproduces most of the figures in @friendly2002corrgrams.


## Setup

```{r setup, results="hide"}
library("knitr")
opts_chunk$set(fig.align="center", fig.width=6, fig.height=6)
options(width=90)
```

The data are 11 measures of performance and salary for 263 baseball players in
the 1986 baseball season in the United States.  The data were used in 1988
Data Expo at the Joint Statistical Meetings.

The first 6 rows of the data and the upper-left corner of the
correlation matrix are given below.

```{r data}
library("corrgram")
head(baseball)
round(cor(baseball[, 5:14], use="pair"),2)
```

## Figure 2

Figure 2 shows two ways to graphically display the correlation matrix using
the `panel.shade()` and `panel.pie()` functions.

```{r fig2}
vars2 <- c("Assists","Atbat","Errors","Hits","Homer","logSal",
           "Putouts","RBI","Runs","Walks","Years")
corrgram(baseball[,vars2], order=TRUE,
         main="Baseball data PC2/PC1 order",
         lower.panel=panel.shade, upper.panel=panel.pie,
         diag.panel=panel.minmax, text.panel=panel.txt)
```

## Figure 3

Figure 3 shows an eigenvector plot of the correlation matrix.  This forms the basis of the orderings of the variables in the corrgram in Figure 4b in the next section, beginning with "AtBat" and then moving counter-clockwise up to "Years".  Note: Eigenvectors are unique only up to a change of sign.

```{r fig3}
baseball.cor <- cor(baseball[,vars2], use='pair')
baseball.eig <- eigen(baseball.cor)$vectors[,1:2]
e1 <- baseball.eig[,1]
e2 <- baseball.eig[,2]
plot(e1,e2,col='white', xlim=range(e1,e2), ylim=range(e1,e2))
text(e1,e2, rownames(baseball.cor), cex=1)
title("Eigenvector plot of baseball data")
arrows(0, 0, e1, e2, cex=0.5, col="red", length=0.1)
```


## Figure 4a, 4b

In figure 4a the variables are sorted in the alphabetical order as given in the data.

In figure 4b, the variables are sorted according to the principal component ordering in Figure 3 to look for possible clustering of the variables.  It is not surprising to see that more times at bat is strongly correlated with a higher number of hits and a higher number of runs.

```{r fig4}
corrgram(baseball[,vars2], main="Baseball data (alphabetic order)")

corrgram(baseball[,vars2], order=TRUE,
         main="Baseball data (PC order)",
         panel=panel.shade, text.panel=panel.txt)
```


## Figure 5

Figure 5 shows a corrgram for all numeric variables in the dataframe.
Non-numeric columns in the data are ignored.

```{r fig5}
corrgram(baseball, order=TRUE, main="Baseball data (PC order)")
```


## Figure 6.

Figure 6 shows a corrgram of automotive data on 74 different models of cars
from 1979.  There are two obvious groups of variables

Note, the arrangement is slightly different from Friendly.

```{r fig6}
corrgram(auto, order=TRUE, main="Auto data (PC order)")
```


## Figure 7.

The inverse of the correlation matrix expresses conditional dependence and
independence of the variables.

The variables are sorted in the same order as in figure 4.  One example
interpretation is: controlling for all other variables, there is still a large
correlation between Years and log Salary.

```{r fig7}
rinv <- function(r){
  # r is a correlation matrix
  # calculate r inverse and scale to correlation matrix
  # Derived from Michael Friendly's SAS code

  ri <- solve(r)
  s <- diag(ri)
  s <- diag(sqrt(1/s))
  ri <- s %*% ri %*% s
  n <- nrow(ri)
  ri <- ri * (2*rep(1,n) - matrix(1, n, n))
  diag(ri) <- 1  # Should already be 1, but could be 1 + epsilon
  colnames(ri) <- rownames(ri) <- rownames(r)
  return(ri)
}

vars7 <- c("Years", "logSal", "Homer", "Putouts", "RBI", "Walks",
           "Runs", "Hits", "Atbat", "Errors", "Assists")
cb <- cor(baseball[,vars7], use="pair")
corrgram(-rinv(cb), main=expression(paste("Baseball data ", R^-1)))

```


## Figure 8

Figure 8 shows a partial independence corrgram for the automotive data, when
Price and MPG are partialed out.

```{r fig8}
require(Matrix) # For block diagonal function

partial <- function(r, xvar){
  # r is a correlation matrix
  # Calculate partial correlation of y|x
  yvar <- setdiff(colnames(r), xvar)
  ri <- r[yvar,yvar] - r[yvar,xvar] %*% solve(r[xvar,xvar]) %*% r[xvar,yvar]
  s <- diag(ri)
  s <- diag(sqrt(1/s))
  ri <- s %*% ri %*% s
  ri <- as.matrix(Matrix::bdiag(ri, r[xvar, xvar]))
  diag(ri) <- 1  # Should already be 1, but could be 1 + epsilon
  colnames(ri) <- rownames(ri) <- c(yvar, xvar)
  return(ri)
}

vars8a <- c("Gratio", "Rep78", "Rep77", "Hroom", "Trunk", "Rseat",
            "Length", "Weight", "Displa", "Turn")
vars8b <- c("MPG", "Price")
vars8 <- c(vars8a, vars8b)
auto.cor <- cor(auto[, vars8], use="pair")
auto.par <- partial(auto.cor, vars8b)
corrgram(auto.par,
         lower.panel=panel.pie, upper.panel=panel.pie,
         main="Auto data, partialing out Price,MPG")
```


## Figure 11

Figure 11 provides another way to display the data, using both ellipses and
loess lines.  Long, narrow ellipses represent high correlations while circular
ellipses represent low correlations.

```{r ellipse}
corrgram(baseball[,vars2], order=TRUE,
         main="Baseball correlation ellipses",
         panel=panel.ellipse,
         text.panel=panel.txt, diag.panel=panel.minmax)
```

# Further examples

Demonstrate density panel, correlation confidence panel

```{r scatter}
corrgram(iris,
         main="Iris data with example panel functions",
         lower.panel=panel.pts, upper.panel=panel.conf,
         diag.panel=panel.density)
```

Demonstrate panel.bar, panel.ellipse, panel.minmax, col.regions

```{r panelbar}
corrgram(auto, order=TRUE,
         main="Auto data (PC order)",
         lower.panel=corrgram::panel.ellipse,
         upper.panel=panel.bar, diag.panel=panel.minmax,
         col.regions=colorRampPalette(c("darkgoldenrod4", "burlywood1",
                                        "darkkhaki", "darkgreen")))
```

## Correlation matrix

The `vote` data is a matrix.

```{r vote}
# 'vote' is a correlation matrix, not a data frame
corrgram(vote, order=TRUE,
         upper.panel=panel.cor, main="vote")
```

## Session information
```{r session}
sessionInfo()
```

## References
