[R] Polychoric Principal Component Analysis (pPCA)

[Peter Maclean]

I have data set with binary responses. I would like to
conduct polychoric principal component analysis (pPCA). I know there are several packages used in PCA but I could not find one that directly estimate pPCA and graph the individuals and variables maps. I will appreciate any help that expand these reproducible scripts.
#How to conduct polychoric principal component analysis pPCA using 
#either of these packages
library(psych) 
library(FactoMineR)
library(nsprcomp)

#Bock and Liberman (1970) data set of 1000 observations of the LSAT
#from psych

data(bock)
responses <- table2df(bock.table[,2:6],count=bock.table[,7],
                labs= paste ("lsat6.",1:5,sep=""))
fix(responses) 
describe(responses)
#Estimate the polychoric correlation matrix to be used in 
#PCA using psych 
W <- polychoric(responses, smooth=TRUE,global=TRUE,polycor=F, 
            ML = FALSE,  std.err=FALSE,progress=TRUE) 
#Regular PCA using stat, psych and FactoMiner, respectively
#There is no option for including the matrix
princomp(responses, cor=TRUE) #What kind of correlation is used here?
 
principal(r = responses, nfactors = 3, rotate = "Promax")
principal(r = W, nfactors = 3, rotate = "Promax") #Do not work

PCA(responses, scale.unit=TRUE, ncp=3, graph=T) 
#How to conduct polychoric principal component analysis using either of #the above package and producing individual and variable factor maps as #above

Peter Maclean
Department of Economics
UDSM