I can calculate the tetrachoric and polycoric correlation coefficients by software, but i don't know What is the tetrachoric or polycoric coefficient furmula.
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You could look at the code that's used to calculate it, by looking, for example, at the source of the polycor package in R - http://rss.acs.unt.edu/Rdoc/library/polycor/R/ or similar in Stata. I would be surprised if it were straightforward. – Jeremy Miles May 09 '13 at 00:07
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different packages use different algorithms to generate these now - so you will get different correlations using say R and Mplus – user20650 May 09 '13 at 02:29
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https://stats.stackexchange.com/questions/3086/differences-between-tetrachoric-and-pearson-correlation – kjetil b halvorsen Jul 31 '17 at 14:24