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# Approximating a partial non-parametric Bayesian correlation in JASP

Hi all, I am interested in augmenting some partial non-parametric correlations with Bayesian tests (my hypothesis is for a lack of association so being able to evaluate support for the null with Bayesian tests is appealing). JASP offers Kendall's tau as a non-parametric alternative for Bayesian correlation but does not support partial correlations.

However, I'm wondering if the following approach based on the manual calculation of a Spearman partial correlation would be a valid alternative. A Spearman partial correlation is calculated by 1) ranking all variables (i.e., X, Y, and Covariate), 2) obtaining residuals from the regressions between the covariate and x & y variables), and 3) performing a Pearson correlation on the residuals. Would I then be able to mimic this approach in the Bayesian module by running a Bayesian Pearson correlation on the residuals, which would be equivalent to a Bayesian Spearman correlation?

My concern is whether the resulting Bayes Factor would be valid or if the calculation of the posterior distribution would be different between the Pearson and Spearman approaches, despite the ranking of variables having been performed prior to obtaining the residuals. I have tried to look into this and found the following paper by the JASP group describing a Bayesian framework for Spearman correlations but unfortunately, I cannot follow the math: https://www.tandfonline.com/doi/full/10.1080/02664763.2019.1709053

The paper also has code to calculate the Bayesian Spearman correlation but unfortunately not partial correlations.

Many thanks!

Michael

• edited August 30

I believe that multiple regression is all about assessing relationships between variables while having "partialled out" some other variable or set of variables. So I think you'll be fine if you're willing to shift your question to something like,

"What is the standardized slope (,i.e., the beta coefficient) for the XY relationship controlling for C?"

Then you could run a Bayesian hierarchical regression by adding Variable C to the null model (under the "Model" option).

R

• edited August 30

Actually, I don't have an answer. I meant to write:

> I believe that multiple regression is all about

> assessing relationships between variables

> while having "partialled out" some other variable

> or set of variables. So I think you'd probably be fine

> if you were willing to shift your question to something like,

> "What is the strength of the XY relationship, controlling for C?"

> Then you could run a two-predictor (X and C) Bayesian

> hierarchical regression by adding Predictor C to the null

> model (under the "Model" option). The value indicating

> "the strength of the XY relationship, controlling for C"

> would be R-squared for the non-null model.

However, that would not address the requirement that it be a

non-parametric analysis.

R

• Thanks, Anderson. Agreed, the challenge here is wanting to use a non-parametric approach. I'm hopeful someone might have additional insights into this!