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phenotypic correlation

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JuanJMV's picture
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Joined: 07/20/2016 - 13:13
phenotypic correlation

Hello,

I am a little bit confused about how to calculate the phenotypic correlation between variable 1 and variable 2, in a bivariate model with one binary variable and one continuous variable.

I mean if I use this: mxEval(cov2cor(V), fitADE, T). I get a value of 0.200 whereas if I calculate the correlation in SPSS (also in R) I get a value of 0.150.

I do not know if I am doing something wrong. Should the results be the same right?
I have tried with different methods, with and without covariables etc… But I get the same value.

Can I get this value from the saturated model?

Thank you so much in advance.

AdminRobK's picture
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Joined: 01/24/2014 - 12:15
biserial vs point-biserial

What you're calculating from OpenMx is a model-expected biserial correlation, which is the correlation between the continuous variable and the normally distributed continuum underlying the binary variable. In contrast, directly calculating the correlation using the default method in most statistical software will give you a point-biserial correlation, which is simply the Pearson correlation between a continuous variable and a binary variable numerically coded with zeroes and ones. In general, the two values won't be the same.

JuanJMV's picture
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Joined: 07/20/2016 - 13:13
Thank you so much.

Thank you so much.

I see, it is the difference between biserial correlation and point-biserial correlation.

Also, Open Mx uses tetrachoric for the correlation between two binary variables and polychoric for ordinal variables right?

What result should I report? I mean what is more correct I know the difference is not too big but I would like to know what is the correct correlation.

AdminRobK's picture
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Joined: 01/24/2014 - 12:15
biserial
I see, it is the difference between biserial correlation and point-biserial correlation.

Also, Open Mx uses tetrachoric for the correlation between two binary variables and polychoric for ordinal variables right?

Essentially, yes. In completely saturated model and with no missing data, the values you get from OpenMx for all four of those types of correlation should match what you get when calculating those correlations a different way. But in general, that won't be true if you're fitting a non-saturated model with OpenMx.

What result should I report? I mean what is more correct I know the difference is not too big but I would like to know what is the correct correlation.

I think reporting the biserial correlation makes more sense, since it reflects what your OpenMx analyses assume about a normally distributed continuum underlying the binary trait. If you want to report it merely as a descriptive statistic, then report it from the saturated model. If it's somehow relevant to your substantive conclusions, then you might want to report it from the "best" model.

JuanJMV's picture
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Joined: 07/20/2016 - 13:13
Thank you!

Thank you!

And how can I get the result from the saturated model?

I mean I can get the correlations with:

mxEval(cov2cor(DZ.covDZ), fit, T) and mxEval(cov2cor(MZ.covMZ), fit, T)

But I do not know how to get the phenotypic correlation for the whole sample at the same time in the saturated model.

Thank you so much in advance.

AdminRobK's picture
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Joined: 01/24/2014 - 12:15
highest-dimensional I guess

Oh, I see. Then I guess I would report the correlation as calculated from the highest-dimensional (most parameters) model that constrains MZ and DZ twin means and variances.

JuanJMV's picture
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Joined: 07/20/2016 - 13:13
Perfect!!

Perfect!!

Thank you so much Rob!

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