# Focused Principal Components Analysis Graphical representation similar to a principal components analysis but adapted to data structured with dependent/independent variables ```r 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. ## Returns 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. ## Author(s) Bruno Falissard, Bill Morphey, Adeline Abbe ## Examples ```r data(sleep) fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+ Gestation.time+Predation+Sleep.exposure+Danger,data=sleep) fpca(y="Paradoxical.sleep",x=c("Body.weight","Brain.weight","Slow.wave.sleep", "Maximum.life.span","Gestation.time","Predation","Sleep.exposure","Danger"),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")) fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+ Gestation.time+Predation+Sleep.exposure+Danger, 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$Paradoxical.sleep~int) resu[i] <- summary(mod)[[4]][2,4]*sign(summary(mod)[[4]][2,1]) } fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+ Gestation.time+Predation+Sleep.exposure+Danger, data=sleep,pvalues=resu) ## A representation with p values ## When input="Cor" or pvalues="Yes" partial is turned to "No" mod <- lm(sleep$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)[[4]][2:9,4]*sign(summary(mod)[[4]][2:9,1]) 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 which come from a multiple linear model ## (here results are difficult to interpret) ```

fpca function