session3.Rmd

---
title: "Training in ade4 in R - Module I: Basic methods"
subtitle: "Multiple correspondence analysis"  
author: "Stéphane Dray"
date: '`r Sys.Date()`'
output:
  xaringan::moon_reader:
    lib_dir: libs
    css:  [custom.css, xaringan-themer.css] 
    nature:
      highlightStyle: github
      highlightLines: true
      countIncrementalSlides: false
    includes:
            before_body: preamble.tex
params:
  correction: FALSE
---

```{r setup, include=FALSE}
options(htmltools.dir.version = FALSE)
knitr::opts_chunk$set(tidy=TRUE, tidy.opts=list(width.cutoff=50), fig.height= 4, fig.width=4, dev='svg', fig.align="center", fig.path = "fig/")
```

```{r correction, include = FALSE}
res.correction <- ifelse(params$correction, "markup", "hide")
```

```{r xaringan-themer, include=FALSE}
library(xaringanthemer)
style_duo(primary_color = "#1F4257", secondary_color = "#F97B64", table_row_even_background_color = "#1F4257")
```

---
# Data

We will analyze the `doubs` data set (see `?doubs`)

```{r}
library(ade4)
library(adegraphics)
data(doubs)
names(doubs)
names(doubs$env)
```
---
# Tranformation into categorical variables

```{r}
fenv <- apply(doubs$env, 2, cut, breaks = 4, labels = 1:4)
fenv <- as.data.frame(fenv, stringsAsFactors = TRUE)
```
---
# Multiple Correspondence Analysis

* Perform MCA
* Display the barplot of eigenvalues

```{r, out.width="30%", include = params$correction, echo = params$correction, results=res.correction}
acm1 <- dudi.acm(fenv, scannf = FALSE)
screeplot(acm1, main = " ", xlab = " ")
```
---
# Graphical representation of MCA results

* Plot the results using the `plot` function

```{r, fig.dim=c(3.5, 3.5), include = params$correction, echo = params$correction, results=res.correction}
plot(acm1, col = TRUE)
```
---
# MCA scores on the geographical map

* Draw maps of MCA scores on the first two axes
* Interpret the maps to describe the environmental structure of the river

```{r, fig.dim=c(4,2), include = params$correction, echo = params$correction, results=res.correction}
mypal <- colorRampPalette(c("#EDF8FB", "#006D2C"))
s.value(doubs$xy, acm1$li[, 1:2], pgrid.draw = FALSE, porigin.draw = FALSE,
    method = "size", symbol = "circle", col = mypal(2),
    ppoints.cex = 1)
```
---
# A look to variables

* Which variables are the most discriminated by the first axes


```{r, echo = params$correction, results=res.correction}
acm1$cr
```
---
# A look to variables

The generic function `score` provides an optimal representation of the maximized criteria

```{r, fig.dim=c(5,3.9)}
score(acm1, type = "boxplot")
```
---
# Hill-Smith analysis

* Build a table mixing quantitative and categorical variables
```{r}
menv <- cbind(fenv[, 1:6], doubs$env[, 7:11])
```
* Perform Hill-Smith analysis
```{r, echo = params$correction, results=res.correction}
hs1 <- dudi.hillsmith(menv, scannf = FALSE)
```
---
# Graphical representation

```{r, fig.dim=c(5,3.9)}
score(hs1, type = "boxplot")
```