D. ASCA

In multiblock: Multiblock Data Fusion in Statistics and Machine Learning

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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.

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.

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

Scores

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

sc <- scores(mod)
head(sc)

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

This is repeated for the second factor.

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.

lo <- loadings(mod)
head(lo)

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

multiblock documentation built on Nov. 18, 2023, 5:06 p.m.