Repository files navigation

Version 0.6.2 ( master branch )

This package provides aggplot2 implementation of the biplot, asimultaneous plot of scores for observations and vectors for variablesfor principal component-like analyses.
The package provides two main functions:ggscreeplot() andggbiplot().

ggbiplot aims to be a drop-in replacement for the standard R functionstats::biplot() with extended functionality for labeling groups,drawing a correlation circle, and adding data ellipsoids. It alsosupports PCA-like objects calculated byFactoMineR::PCA(),ade4::dudi.pca() andMASS::lda().

The package was originally developed by Vince Vu athttps://github.com/vqv/ggbiplot. That development was supported inpart by NSF Postdoctoral Fellowship DMS-0903120 from 2009-2012. Thecurrent version, now on CRAN, will be the locus of further development.

You can install the latest CRAN version, or install from GitHub as shownbelow.

Load packages:

library(ggplot2)library(ggbiplot)library(dplyr)library(corrplot)# set ggplot2 themetheme_set(theme_minimal(base_size=14))

Thecrime data gives rates of various serious crimes in each of the 50U. S. states, originally from the United States Statistical Abstracts(1970).

Let’s take a quick look at the correlations among these, usingcorrplot::corrplot() and showing each correlation by an ellipse whoseeccentricity and shading represents the value of the correlation.

data(crime)crime|>dplyr::select(where(is.numeric))|>   cor()|>   corrplot(method="ellipse",tl.srt=0)

The correlations are all positive. Note also that the variables in thedataset are ordered in seriousness or violence, ranging from murder toauto theft.

Carry out a PCA:

crime.pca<-crime|>dplyr::select(where(is.numeric))|>  prcomp(scale.=TRUE)crime.pca#> Standard deviations (1, .., p=7):#> [1] 2.029 1.113 0.852 0.563 0.508 0.471 0.352#>#> Rotation (n x k) = (7 x 7):#>             PC1     PC2     PC3     PC4     PC5     PC6     PC7#> murder   -0.300 -0.6292 -0.1782  0.2321  0.5381  0.2591  0.2676#> rape     -0.432 -0.1694  0.2442 -0.0622  0.1885 -0.7733 -0.2965#> robbery  -0.397  0.0422 -0.4959  0.5580 -0.5200 -0.1144 -0.0039#> assault  -0.397 -0.3435  0.0695 -0.6298 -0.5067  0.1724  0.1917#> burglary -0.440  0.2033  0.2099  0.0576  0.1010  0.5360 -0.6481#> larceny  -0.357  0.4023  0.5392  0.2349  0.0301  0.0394  0.6017#> auto     -0.295  0.5024 -0.5684 -0.4192  0.3698 -0.0573  0.1470

The biplot, using default scaling (standardized components), andlabeling the states by their state abbreviation:

ggbiplot(crime.pca,labels=crime$st ,circle=TRUE,varname.size=4,varname.color="red")

The directions of the principal components are arbitrary; we are free toreflect the variable vectors and component scores to facilitateinterpretation. Also, there seem to be differences among regions of theU.S., which can be visualized using data ellipses for the componentscores. Thegroups argument allows the observations to colored bygroup and to summarized by groups.

crime.pca<- reflect(crime.pca)ggbiplot(crime.pca,groups=crime$region,labels=crime$st,labels.size=4,var.factor=1.4,ellipse=TRUE,ellipse.level=0.5,ellipse.alpha=0.1,circle=TRUE,varname.size=4,varname.color="black")+  labs(fill="Region",color="Region")+  theme(legend.direction='horizontal',legend.position='top')

The interpretation of the data is now clear.

• The first dimension, accounting for 58.8% of variance, can be seen torepresentoverall crime rate, with Nevada (NV) at the high end andNorth Dakota (ND), South Dakota (SD) and West Virginia (WV) at the lowend.

• The second dimension, accounting for 17.7% of variance represents acontrast betweenpersonal crime vs. property crime. On thisdimension, Massachusetts (MA), Rhode Island (RI) are opposed toMississippi (MS), Alabama (AL), Louisiana (LA) and South Carolina(SC).

• The regions are represented by the differences in the centers of thedata ellipses for the scores. Southern states are highest on murder,assault and rape, while the Northeast states are highest on auto theftand larceny.

• In this standardized view, the angles between variable vectorsapproximate the correlations among the variables, according to$\cos (\text{angle}) \approx r$. Thus,murder andauto, nearly$90^o$ reflect a near 0 correlation.

Thewine data contains results of a chemical analysis of wines grownin the same region in Italy, derived from three different cultivars. Theanalysis determined the quantities of 13 chemical constituents found ineach of the three types of wines. The grape varieties (cultivars),barolo,barbera, andgrignolino, are given inwine.class.

What can we understand about the differences among these wines from abiplot?

data(wine)wine.pca<- prcomp(wine,scale.=TRUE)ggscreeplot(wine.pca)

Hmm. The screeplot shows that more than two dimensions are necessary toaccount for most of the variance.

Plot the first two PCA dimensions, accounting for 55% of the variance.

ggbiplot(wine.pca,obs.scale=1,var.scale=1,groups=wine.class,varname.size=4,ellipse=TRUE,circle=TRUE)+  labs(fill="Cultivar",color="Cultivar")+  theme(legend.direction='horizontal',legend.position='top')

The three cultivars are arranged along the first dimension, in the orderbarolo < grignolino < barbera. These are distinguished largely by acontrast between (Phenols,Flav) vs. (NonFlavPhenols,AlcAsh).The second dimension is represented by the cluster of variablesMg,Alcohol,Ash,Color, which distinguishes grignolino from the othertwo.

The classic iris data is widely used for examples of multivariateanalysis and biplots, so let’s use it here.

data(iris)iris.pca<- prcomp (~Sepal.Length+Sepal.Width+Petal.Length+Petal.Width,data=iris,scale.=TRUE)summary(iris.pca)#> Importance of components:#>                         PC1   PC2    PC3     PC4#> Standard deviation     1.71 0.956 0.3831 0.14393#> Proportion of Variance 0.73 0.229 0.0367 0.00518#> Cumulative Proportion  0.73 0.958 0.9948 1.00000

Plot the first two dimensions:

iris.gg<-ggbiplot(iris.pca,obs.scale=1,var.scale=1,groups=iris$Species,point.size=2,varname.size=5,varname.color="black",varname.adjust=1.2,ellipse=TRUE,circle=TRUE)+  labs(fill="Species",color="Species")+  theme_minimal(base_size=14)+  theme(legend.direction='horizontal',legend.position='top')iris.gg

It is possible to add annotations to the biplot by making use of thefact thatggplot() returns a lot of information in the"gg" object.In particular, the$data component contains the scores on theprincipal components that are plotted as points here. Here we add directlabels for the groups and suppress the legend.

# get means of coordinates by groupgroup.labs<-iris.gg$data|>  summarise(xvar= mean(xvar),yvar= mean(yvar),.by=groups)group.labs#>       groups   xvar   yvar#> 1     setosa -2.217 -0.288#> 2 versicolor  0.495  0.548#> 3  virginica  1.723 -0.260

Now, just usegeom_label to draw labels for the groups.

iris.gg+ geom_label(data=group.labs,                     aes(x=xvar,y=yvar,label=groups),size=5)+  theme(legend.position="none")