Why are polychoric correlation coefficients in matrices calculated by different R packages slightly different for the same data?

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I calculated polychoric correlation matrices for the same data frame (20 ordinal variables, 190 missing values) in R, using three different packages and the coefficients for same variables are slightly different from each other.

I used the lavCor function from "lavaan" (I did list the ordinal variables when calling the function), polychoric function from "psych" (1.9.1) (took the rhos), and cor_auto function from "qgraph" (which is supposed to automatically calculate polychoric correlations for ordinal data). I am confused because I thought they were supposed to give exactly the same results. I read package documentations but could not find anything that helped me understand why. Could anyone let me know why this happens? I am sure I am missing some tiny difference between those, but I cannot figure it out.

PS: I guess this could have happened because psych package adjusts missing values (I have 190) using the correction for continuity, but I still do not understand why qgraph yields different results than lavaan as qgraph says it uses lavaan's lavCor function to calculate polychoric correlations.

Thanks!!

depanx<-data[1:20]

cor.depanx<-cor_auto(depanx)

polychor<-polychoric(depanx)
polymat<-polychor$rho

lav<-lavCor(depanx,ordered=c("unh","enj","trd","rst","noG","cry","cnc","htd","bdp","lnl","lov",
                             "cmp","wrg","pst","sch","dss","hlt","bad","ftr","oth"))

# as a result, matrices "cor.depanx", "polymat", and "lav" are different from each other.
psych r
1 Answers

Nice question! I do not know what the "data" dataset in you example is, but i recreate the two possible scenarios, which have most probably caused the discrepancy between cor_auto and lavCor results. In summary, first you must set the "ordinalLevelMax" argument in cor_auto based on your data and second you need to synchronize the "missing" argument in the two functions. Detailed explanation in the code snippet below:

depanx<-data.frame(lapply(1:5,function(x)sample(1:6,100,replace = T)),
stringsAsFactors = F)
colnames(depanx)=LETTERS[1:5]
lav<-lavaan::lavCor(depanx,ordered=colnames(depanx))
cor.depanx<-cor_auto(depanx)
all(lav==cor.depanx)#TRUE

#The first argument in cor auto, which you need to pay attention to is 
#"ordinalLevelMax". #It is set to 7 by default in cor_auto,
#so any variable with levels more than 7 is sent to lavCor as plain numeric and not 
#ordinal. 
#Now we create the same dataset with 8 level variables. lavCor detects all as ordinal,
#since we have labeled them as so by "ordered" argument of lavCor, so it uses 
#ploychorial
#correlations. Since "ordinalLevelMax" in cor_auto is 7 by default and you have not 
#changed it,
#cor_auto detect none as ordinaland does not send them to lavCor as Ordinalvariables, 
#so Lavcor computes pearson correlations between them,all.
depanx2<-data.frame(lapply(1:5,function(x)sample(1:8,100,replace =T)),
stringsAsFactors = F)
colnames(depanx2)=LETTERS[1:5]
lav2<-lavaan::lavCor(depanx2,ordered=colnames(depanx2))
cor.depanx2<-cor_auto(depanx2)
all(lav2==cor.depanx2)#FALSE

# the next argument you must synchronise in lavCor and cor_auto is the "missing",
#which is by default set to "pairwise" and "listwise" in cor_auto and lavCor, 
#respectively.
#here we set row 10:20 value of the fifth variable to NA, without synchronizing the 
#argument
depanx3<-data.frame(lapply(1:5,function(x)sample(1:6,100,replace =T)),
stringsAsFactors = F)
colnames(depanx3)=LETTERS[1:5]
depanx3[10:20,5]<-NA
lav3<-lavaan::lavCor(depanx3,ordered=colnames(depanx3))
cor.depanx3<-cor_auto(depanx3)
all(lav3==cor.depanx3)#FALSE
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