From everything I have read, both tetrachoric and polychoric correlations assume normal distributions. However, the data I want to conduct these correlations with is not normally distributed. Does anyone know if there is an alternative approach to using tetrachoric and polychoric correlations when there is non-normal data?
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$\begingroup$ john-uebersax.com/stat/skewed.htm $\endgroup$– user20650Commented Mar 28, 2022 at 14:55
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$\begingroup$ @user20650 Does this mean that in order to do a tetrachoric or polychoric correlation that if the distro is not normal that at least one of the variables has to be latent? (mine are not) $\endgroup$– SurpriseDogCommented Mar 28, 2022 at 17:29
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$\begingroup$ I'm not sure that I understand. Both tetrachoric and polychoric correlations hypothesis an underlying latent variable, but the observed variables are ordinal. $\endgroup$– user20650Commented Mar 28, 2022 at 20:17
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$\begingroup$ @user20650 There is no latent variable. I'm looking at two sets of binary scores to see if they're correlated with each other. Is there a better approach? $\endgroup$– SurpriseDogCommented Mar 29, 2022 at 19:44
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$\begingroup$ You don't observe the latent variable. Tetrachoric correlations assume that there is an underlying latent normal variable which generate the observed variable, which in this case are binary variables. So that seems to fit with what you have. But if you are just wanting some measure of association , perhaos a $\chi^2$ test is enough? $\endgroup$– user20650Commented Mar 29, 2022 at 21:12
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