Lognormalising Ordinal Data

General
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Hi All,

I have some ordinal data that I'd like to transform into a continuous score following Chen and Wang (2014) https://downloads.hindawi.com/journals/tswj/2014/304213.pdf

I don't have much experience with these types of transformations in R, and I appreciate there might be pitfalls.

Would it be possible for someone to demonstrate how to place some ordinal data on the log-normal scale using some toy data?

Would appreciate the help

X1 <- c("2", "1", "2", "3", "2", "2", "3", "2", "1", "1")
X2 <- c("1", "2", "3", "2", "2", "3", "3","2", "2", "2")

df <- data.frame(X1, X2)
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