```
burt <- psychTools::burt
bs <- cor.smooth(psychTools::burt) #burt data set is not positive definite
plot(burt[lower.tri(burt)],bs[lower.tri(bs)],ylab="smoothed values",xlab="original values")
abline(0,1,lty="dashed")
round(burt - bs,3)
fa(burt,2) #this throws a warning that the matrix yields an improper solution
#Smoothing first throws a warning that the matrix was improper,
#but produces a better solution
fa(cor.smooth(burt),2)
#this next example is a correlation matrix from DeLeuw used as an example
#in Knol and ten Berge.
#the example is also used in the nearcor documentation
cat("pr is the example matrix used in Knol DL, ten Berge (1989)\n")
pr <- matrix(c(1, 0.477, 0.644, 0.478, 0.651, 0.826,
0.477, 1, 0.516, 0.233, 0.682, 0.75,
0.644, 0.516, 1, 0.599, 0.581, 0.742,
0.478, 0.233, 0.599, 1, 0.741, 0.8,
0.651, 0.682, 0.581, 0.741, 1, 0.798,
0.826, 0.75, 0.742, 0.8, 0.798, 1),
nrow = 6, ncol = 6)
sm <- cor.smooth(pr)
resid <- pr - sm
# several goodness of fit tests
# from Knol and ten Berge
tr(resid %*% t(resid)) /2
# from nearPD
sum(resid^2)/2
```

Run the code above in your browser using DataCamp Workspace