[R] polychoric correlation: issue with coefficient sign

[Jim Lemon]

Dorothee wrote:
> Hello,
>
> I am running polychoric correlations on a dataset composed of 12 ordinal and
> binary variables (N =384), using the polycor package.
> One of the association (between 2 dichotomous variables) is very high using
> the 2-step estimate (0.933 when polychoric run only between the two
> variables; but 0.801 when polychoric run on the 12 variables). The same
> correlation run with ML estimate returns a singularity message.
>
> First, I would like to know why the estimations between only the two
> dichotomous variables and with all the variables at once (with the 2-step
> estimate) returns slightly different results.
>
> Secondly, when i checked back the distribution of these two dichotomous
> variables they appear about symmetrically opposed. Therefore, one should
> indeed expect a strong association between them, but a negative one, isn't
> it? Why does the polychoric correlation returns a positive coefficient? What
> does it mean for the rest of the coefficients, should i trust them?
>
> I have to say I'm new to R and not very strong in statistics, I hope I
> haven't posted a stupid question...
>   
Hi Dorothee,
This may be similar to a problem I encountered with the biserial.cor 
function, where the default specification of which value of the 
dichotomous variable to use as the reference value gave me a correlation 
coefficient with an apparently reversed sign. It might be that your the 
values of your categorial variable are not in the order you assume.

Jim