Tag: correlation

Partial Correlation in R

When computing the correlation between two variables, an interesting question is how it will be affected if we control for another variable(s), where control means hold constant.

R offers the function pcor.test() in the ppcor package. This function has the format pcor.test(X,Y,Z) where X and Y are the variables for which we want to compute the correlation, while Z consists of column vectors containing the controlling variable(s).

In the link below, we apply pcor.test() to a dataset and compare it will computing correlations by group. The results show that computing correlations by group, provides useful insights, while pcor.test() does not.

 

Code for partial correlation and correlation by group

Correlation of the columns of a dataframe in R

1. Columns contain numerical values.

Here we can use the function cor().

Example:

> library(MASS)
> cor(trees)
Girth Height Volume
Girth 1.0000000 0.5192801 0.9671194
Height 0.5192801 1.0000000 0.5982497
Volume 0.9671194 0.5982497 1.0000000

2. Some columns contain numerical and some contain ordinal values.

Here we can use the function hetcor() in R package polycor. This function computes Pearson correlations between numeric columns, polyserial correlations between numeric and ordinal variables, and polychoric correlations between ordinal variables. We will try it on dataset quine in the faraway package.

Example:

>library(faraway)
> library(polycor)
> quine[1:4,]
Eth Sex Age Lrn Days
1 A M F0 SL 2
2 A M F0 SL 11
3 A M F0 SL 14
4 A M F0 AL 5
> hetcor(quine)

Two-Step Estimates

Correlations/Type of Correlation:
Eth Sex Age Lrn Days
Eth 1 Polychoric Polychoric Polychoric Polyserial
Sex 0.008333 1 Polychoric Polychoric Polyserial
Age -0.02581 -0.08348 1 Polychoric Polyserial
Lrn 0.03389 -0.2393 -0.3187 1 Polyserial
Days -0.3504 0.1048 0.1773 0.05657 1

Standard Errors:
Eth Sex Age Lrn
Eth
Sex 0.1305
Age 0.1109 0.1103
Lrn 0.1307 0.1259 0.1026
Days 0.09246 0.1025 0.08507 0.1039

n = 146

P-values for Tests of Bivariate Normality:
Eth Sex Age Lrn
Eth
Sex <NA>
Age 0.8355 0.01814
Lrn <NA> <NA> 7.895e-11
Days 0.008092 0.009787 0.007213 0.005257