fpca

From psy v1.1
0th

Percentile

Focused Principal Components Analysis

Graphical representation similar to a principal components analysis but adapted to data structured with dependent/independent variables

Keywords
multivariate
Usage
fpca(formula=NULL,y=NULL, x=NULL, data, cx=0.75, pvalues="No", partial="Yes", input="data", contraction="No", sample.size=1)
Arguments
formula
"model" formula, of the form y ~ x
y
column number of the dependent variable
x
column numbers of the independent (explanatory) variables
data
name of datafile
cx
size of the lettering (0.75 by default, 1 for bigger letters, 0.5 for smaller)
pvalues
vector of prespecified pvalues (pvalues="No" by default) (see below)
partial
partial="Yes" by default, corresponds to the original method (see below)
input
input="Cor" for a correlation matrix (input="data" by default)
contraction
change the aspect of the diagram, contraction="Yes" is convenient for large data set (contraction="No" by default)
sample.size
to be specified if input="Cor"
Details

This representation is close to a Principal Components Analysis (PCA). Contrary to PCA, correlations between the dependent variable and the other variables are represented faithfully. The relationships between non dependent variables are interpreted like in a PCA: correlated variables are close or diametrically opposite (for negative correlations), independent variables make a right angle with the origin. The focus on the dependent variable leads formally to a partialisation of the correlations between the non dependent variables by the dependent variable (see reference). To avoid this partialisation, the option partial="No" can be used. It may be interesting to represent graphically the strength of association between the dependent variable and the other variables using p values coming from a model. A vector of pvalue may be specified in this case.

Value

A plot (q plots in fact).

References

Falissard B, Focused Principal Components Analysis: looking at a correlation matrix with a particular interest in a given variable. Journal of Computational and Graphical Statistics (1999), 8(4): 906-912.

• fpca
Examples
data(sleep)

## focused PCA of the duration of paradoxical sleep (dreams, 5th column)
## against constitutional variables in mammals (columns 2, 3, 4, 7, 8, 9, 10, 11).
## Variables inside the red cercle are significantly correlated
## to the dependent variable with p<0.05.
## Green variables are positively correlated to the dependent variable,
## yellow variables are negatively correlated.
## There are three clear clusters of independent variables.

corsleep <- as.data.frame(cor(sleep[,2:11],use="pairwise.complete.obs"))
data=corsleep,input="Cor",sample.size=60)

## when missing data are numerous, the representation of a pairwise correlation
## matrix may be preferred (even if mathematical properties are not so good...)

numer <- c(2:4,7:11)
l <- length(numer)
resu <- vector(length=l)
for(i in 1:l)
{
int <- sleep[,numer[i]]
mod <- lm(sleep$Paradoxical.sleep~int) resu[i] <- summary(mod)[][2,4]*sign(summary(mod)[][2,1]) } fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+Gestation.time+Predation+Sleep.exposure+Danger, data=sleep,pvalues=resu) ## A representation with p values ## When input="Cor" or pvalues="Yes" partial is turned to "No" mod <- lm(sleep$Paradoxical.sleep~sleep$Body.weight+sleep$Brain.weight+
sleep$Slow.wave.sleep+sleep$Maximum.life.span+sleep$Gestation.time+ sleep$Predation+sleep$Sleep.exposure+sleep$Danger)
resu <-  summary(mod)[][2:9,4]*sign(summary(mod)[][2:9,1])