Bayesian partial correlations

[JulianGaviriaL]

1. I obtain the following results from the Bayesian correlation test of "Sepal.Length", "Sepal.Width", "Petal.Length" (iris dataset):

require(easystats)
require(BayesFactor)
require(see)

d<-correlation(iris, select=c("Sepal.Length", "Sepal.Width", "Petal.Length"), bayesian = TRUE)

Parameter1 | Parameter2 | rho | 95% CI | pd | % in ROPE | Prior | BF

Sepal.Length | Sepal.Width | -0.11 | [-0.27, 0.04] | 91.62% | 44.38% | Beta (3 +- 3) | 0.509
Sepal.Length | Petal.Length | 0.86 | [ 0.82, 0.90] | 100%*** | 0% | Beta (3 +- 3) | 2.14e+43***
Sepal.Width | Petal.Length | -0.41 | [-0.54, -0.28] | 100%*** | 0% | Beta (3 +- 3) | 3.49e+05***

My aim is to compute bayesian partial correlations. I tried 2 different codes:

e<-correlation(iris, select=c("Sepal.Length", "Sepal.Width", "Petal.Length"), bayesian = TRUE,partial_bayesian = TRUE)
f<-correlation(iris, select=c("Sepal.Length", "Sepal.Width", "Petal.Length"), bayesian = TRUE,partial = TRUE, partial_bayesian = TRUE)

Which one yields the most reliable results?

e

Correlation Matrix (pearson-method)

Parameter1 | Parameter2 | rho | 95% CI | pd | % in ROPE | Prior | BF

Sepal.Length | Sepal.Width | -0.11 | [-0.25, 0.05] | 91.42% | 44.55% | Beta (3 +- 3) | 0.509
Sepal.Length | Petal.Length | 0.86 | [ 0.82, 0.90] | 100%*** | 0% | Beta (3 +- 3) | 2.14e+43***
Sepal.Width | Petal.Length | -0.41 | [-0.55, -0.28] | 100%*** | 0% | Beta (3 +- 3) | 3.49e+05***

Observations: 150

f

Correlation Matrix (pearson-method)

Parameter1 | Parameter2 | rho | 95% CI | pd | % in ROPE | Prior | BF

Sepal.Length | Sepal.Width | 0.57 | [ 0.45, 0.66] | 100%*** | 0% | Beta (3 +- 3) | 6.96e+11***
Sepal.Length | Petal.Length | 0.91 | [ 0.87, 0.93] | 100%*** | 0% | Beta (3 +- 3) | 2.81e+55***
Sepal.Width | Petal.Length | -0.65 | [-0.74, -0.56] | 100%*** | 0% | Beta (3 +- 3) | 4.73e+17***

Observations: 150

2. I assume that the correlation value (rho) of "Sepal.Length" | Sepal.Width" is adjusted for the linear effect of "Petal.Length".
   2.a) How does it works when I have 4 or a greater number of variables?
   2.b) Would it be possible to determine which variable (either "Petal.Length" or "Petal.Width") controls the correlation between "Sepal.Length" | Sepal.Width"?

g<-correlation(iris, select=c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width"), bayesian = TRUE)