```
#if(require(mnormt)) {
data(bock)
tetrachoric(lsat6)
polychoric(lsat6) #values should be the same
tetrachoric(matrix(c(44268,193,14,0),2,2)) #MPLUS reports.24
#Do not apply continuity correction -- compare with previous analysis!
tetrachoric(matrix(c(44268,193,14,0),2,2),correct=0)
#the default is to add correct=.5 to 0 cells
tetrachoric(matrix(c(61661,1610,85,20),2,2)) #Mplus reports .35
tetrachoric(matrix(c(62503,105,768,0),2,2)) #Mplus reports -.10
tetrachoric(matrix(c(24875,265,47,0),2,2)) #Mplus reports 0
polychoric(matrix(c(61661,1610,85,20),2,2)) #Mplus reports .35
polychoric(matrix(c(62503,105,768,0),2,2)) #Mplus reports -.10
polychoric(matrix(c(24875,265,47,0),2,2)) #Mplus reports 0
#Do not apply continuity correction- compare with previous analysis
tetrachoric(matrix(c(24875,265,47,0),2,2), correct=0)
polychoric(matrix(c(24875,265,47,0),2,2), correct=0) #the same result
#examples from Kirk 1973
#note that Kirk's tables have joint probability followed by marginals, but
#tetrachoric needs marginals followed by joint probability
tetrachoric(c(.5,.5,.333333)) #should be .5
tetrachoric(c(.5,.5,.1150267)) #should be -.75
tetrachoric(c(.5,.5,.397584)) #should e .8
tetrachoric(c(.158655254,.158655254,.145003)) #should be .99
#the example from Olsson, 1979
x <- as.table(matrix(c(13,69,41,6,113,132,0,22,104),3,3))
polychoric(x,correct=FALSE)
#Olsson reports rho = .49, tau row = -1.77, -.14 and tau col = -.69, .67
#give a vector of two marginals and the comorbidity
tetrachoric(c(.2, .15, .1))
tetrachoric(c(.2, .1001, .1))
#} else {
# message("Sorry, you must have mnormt installed")}
# 4 plots comparing biserial to point biserial and latent Pearson correlation
set.seed(42)
x.4 <- sim.congeneric(loads =c(.9,.6,.3,0),N=1000,short=FALSE)
y <- x.4$latent[,1]
for(i in 1:4) {
x <- x.4$observed[,i]
r <- round(cor(x,y),1)
ylow <- y[x<= 0]
yhigh <- y[x > 0]
yc <- c(ylow,yhigh)
rpb <- round(cor((x>=0),y),2)
rbis <- round(biserial(y,(x>=0)),2)
ellipses(x,y,ylim=c(-3,3),xlim=c(-4,3),pch=21 - (x>0),
main =paste("r = ",r,"rpb = ",rpb,"rbis =",rbis))
dlow <- density(ylow)
dhigh <- density(yhigh)
points(dlow$y*5-4,dlow$x,typ="l",lty="dashed")
lines(dhigh$y*5-4,dhigh$x,typ="l")
}
#show non-symmeteric results
test1 <- tetrachoric(psychTools::ability[,1:4],psychTools::ability[,5:10])
test2 <- polychoric(psychTools::ability[,1:4],psychTools::ability[,5:10])
all <- tetrachoric(psychTools::ability[,1:10])
```

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