🚀 go-pugleaf

In <STAT-L%93063012172631@VM1.MCGILL.CA> "Gary L...r" <GARYLAUT@UGA.BITNET> writes:

>Tony Downing asks about polychoric correlation...

>The polychoric correlation for the dichotomous item score case is a tetrachoric
>correlation.  In effect, it is an estimate of what the correlation would be
>assuming that the two dichotomously scored items really reflect latent
>variables which have a continuous (and normal) distribution of values.  The
>tetrachoric is the correlation of the two continuous latent variables.

>Some have suggested that conversion of the raw phi (pearson) inter-item
>correlations to tetrachoric correlations can eliminate such artifacts.

It is worth noting that Nunnally, for example, although he describes
tetrachoric correlations is pretty scathing about their use, stating
firstly that they give very inaccurate estimates of PM correlations
and secondly that they should not be used in multivariate analysis.  In
particular he criticises their use in factor analysis because their
use as estimates is "not mathematically proper".
He concludes that although they might be used in mathematical models,
"they definitely should not be used to determine the correlation
between sets of empirical data".

Best wishes

Charles Johnson