---
title: "D. ASCA"
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```{r, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width=6, 
  fig.height=4
)
# Legge denne i YAML på toppen for å skrive ut til tex
#output: 
#  pdf_document: 
#    keep_tex: true
# Original:
#  rmarkdown::html_vignette:
#    toc: true
```

```{r setup}
library(multiblock)
```

# ANOVA Simultaneous Component Analysis -- ASCA

The following example uses a simulated dataset for showcasing some of the possibilities of the ASCA method.


## Simulated data

Two categorical factors and a covariate are simulated together with a standard normal set of 10 responses.

```{r cars}
set.seed(1)
dataset   <- data.frame(y = I(matrix(rnorm(24*10), ncol = 10)), 
                        x = factor(c(rep(2,8), rep(1,8), rep(0,8))), 
                        z = factor(rep(c(1,0), 12)), w = rnorm(24))
colnames(dataset$y) <- paste('Var', 1:10, sep = " ")
rownames(dataset)   <- paste('Obj', 1:24, sep = " ")
str(dataset)
```

## Formula interface

This ASCA implementation uses R's formula interface for model specification. This means that the first argument is a formula with response on the left and design on the right, separated by a tilde operator, e.g. _y ~ x + z_ or _assessment ~ assessor + candy_. The names in the formula refer to variables in a data.frame (or list). Separation with plus (_+_) adds main effects to the model, while separation by stars (_\*_) adds main effects and interactions, e.g. _y ~ x \* z_. Colons (_:_) can be used for explicit interactions, e.g. _y ~ x + z + x:z_. More complicated formulas exist, but only a simple subset is supported by _asca_.


## ASCA modelling

A basic ASCA model having two factors is fitted and printed as follows.

```{r}
mod <- asca(y~x+z, data = dataset)
print(mod)
```

## Scores

Scores for first factor are extracted and a scoreplot with confidence ellipsoids is produced.

```{r}
sc <- scores(mod)
head(sc)

scoreplot(mod, legendpos = "topleft", ellipsoids = "confidence")
```

This is repeated for the second factor.

```{r}
sc <- scores(mod, factor = "z")
head(sc)

scoreplot(mod, factor = "z", ellipsoids = "confidence")
```

## Loadings

A basic loadingplot for the first factor is generated using graphics from the _pls_ package.

```{r}
lo <- loadings(mod)
head(lo)

loadingplot(mod, scatter = TRUE, labels = 'names')
```