Intraclass Correlation in Python Module?
The R package psych has an implementation of the Intraclass Correlations (ICC) that calculates many types of variants including ICC(1,1), ICC(1,k), ICC(2,1), ICC(2,k), ICC(3,1) and ICC(3,k) plus other metrics.
This page has a good comparison between the different variants,
You can use the R ICC function via rpy2 package.
Example:
- First install
psychandlme4in R:
install.packages("psych")
install.packages("lme4")
- Calculate ICC coefficients in Python using rpy2:
import rpy2
from rpy2.robjects import IntVector, pandas2ri
from rpy2.robjects.packages import importr
psych = importr("psych")
values = rpy2.robjects.r.matrix(
IntVector(
[9, 2, 5, 8,
6, 1, 3, 2,
8, 4, 6, 8,
7, 1, 2, 6,
10, 5, 6, 9,
6, 2, 4, 7]),
ncol=4, byrow=True
)
icc = psych.ICC(values)
# Convert to Pandas DataFrame
icc_df = pandas2ri.rpy2py(icc[0])
Results:
type ICC F df1 df2 p lower bound upper bound
Single_raters_absolute ICC1 0.165783 1.794916 5.0 18.0 0.164720 -0.132910 0.722589
Single_random_raters ICC2 0.289790 11.026650 5.0 15.0 0.000135 0.018791 0.761107
Single_fixed_raters ICC3 0.714829 11.026650 5.0 15.0 0.000135 0.342447 0.945855
Average_raters_absolute ICC1k 0.442871 1.794916 5.0 18.0 0.164720 -0.884193 0.912427
Average_random_raters ICC2k 0.620080 11.026650 5.0 15.0 0.000135 0.071153 0.927240
Average_fixed_raters ICC3k 0.909311 11.026650 5.0 15.0 0.000135 0.675657 0.985891
There are several implementations of the ICC in R. These can be used from Python via the rpy2 package. Example:
from rpy2.robjects import DataFrame, FloatVector, IntVector
from rpy2.robjects.packages import importr
from math import isclose
groups = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,
4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8]
values = [1, 2, 0, 1, 1, 3, 3, 2, 3, 8, 1, 4, 6, 4, 3,
3, 6, 5, 5, 6, 7, 5, 6, 2, 8, 7, 7, 9, 9, 9, 9, 8]
r_icc = importr("ICC")
df = DataFrame({"groups": IntVector(groups),
"values": FloatVector(values)})
icc_res = r_icc.ICCbare("groups", "values", data=df)
icc_val = icc_res[0] # icc_val now holds the icc value
# check whether icc value equals reference value
print(isclose(icc_val, 0.728, abs_tol=0.001))
You can find an implementation at ICC or Brain_Data.icc
The pengouin library computes ICC in 6 different ways, along with associated confidence levels and p values.
You can install it with pip install pingouin or conda install -c conda-forge pingouin
import pingouin as pg
data = pg.read_dataset('icc')
icc = pg.intraclass_corr(data=data, targets='Wine', raters='Judge',
ratings='Scores')
data.head()
| | Wine | Judge | Scores |
|---:|-------:|:--------|---------:|
| 0 | 1 | A | 1 |
| 1 | 2 | A | 1 |
| 2 | 3 | A | 3 |
| 3 | 4 | A | 6 |
| 4 | 5 | A | 6 |
| 5 | 6 | A | 7 |
| 6 | 7 | A | 8 |
| 7 | 8 | A | 9 |
| 8 | 1 | B | 2 |
| 9 | 2 | B | 3 |
icc
| | Type | Description | ICC | F | df1 | df2 | pval | CI95% |
|---:|:-------|:------------------------|------:|-------:|------:|------:|------------:|:-------------|
| 0 | ICC1 | Single raters absolute | 0.773 | 11.199 | 5 | 12 | 0.000346492 | [0.39, 0.96] |
| 1 | ICC2 | Single random raters | 0.783 | 27.966 | 5 | 10 | 1.42573e-05 | [0.25, 0.96] |
| 2 | ICC3 | Single fixed raters | 0.9 | 27.966 | 5 | 10 | 1.42573e-05 | [0.65, 0.98] |
| 3 | ICC1k | Average raters absolute | 0.911 | 11.199 | 5 | 12 | 0.000346492 | [0.65, 0.99] |
| 4 | ICC2k | Average random raters | 0.915 | 27.966 | 5 | 10 | 1.42573e-05 | [0.5, 0.99] |
| 5 | ICC3k | Average fixed raters | 0.964 | 27.966 | 5 | 10 | 1.42573e-05 | [0.85, 0.99] |