Intraclass Correlation in Python Module?

Question

I\'m looking to calculate intraclass correlation (ICC) in Python. I haven\'t been able to find an existing module that has this feature. Is there an alternate name, or should I

Answer 1

Based on Brain_Data, I modified the code in order to calculate the correlation coefficients ICC(2,1), ICC(2,k), ICC(3,1) or ICC(3,k) for data input as a table Y (subjects in rows and repeated measurements in columns).

import os
import numpy as np
from numpy import ones, kron, mean, eye, hstack, dot, tile
from numpy.linalg import pinv

def icc(Y, icc_type='ICC(2,1)'):
    ''' Calculate intraclass correlation coefficient

    ICC Formulas are based on:
    Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: uses in
    assessing rater reliability. Psychological bulletin, 86(2), 420.
    icc1:  x_ij = mu + beta_j + w_ij
    icc2/3:  x_ij = mu + alpha_i + beta_j + (ab)_ij + epsilon_ij
    Code modifed from nipype algorithms.icc
    https://github.com/nipy/nipype/blob/master/nipype/algorithms/icc.py

    Args:
        Y: The data Y are entered as a 'table' ie. subjects are in rows and repeated
            measures in columns
        icc_type: type of ICC to calculate. (ICC(2,1), ICC(2,k), ICC(3,1), ICC(3,k)) 
    Returns:
        ICC: (np.array) intraclass correlation coefficient
    '''

    [n, k] = Y.shape

    # Degrees of Freedom
    dfc = k - 1
    dfe = (n - 1) * (k-1)
    dfr = n - 1

    # Sum Square Total
    mean_Y = np.mean(Y)
    SST = ((Y - mean_Y) ** 2).sum()

    # create the design matrix for the different levels
    x = np.kron(np.eye(k), np.ones((n, 1)))  # sessions
    x0 = np.tile(np.eye(n), (k, 1))  # subjects
    X = np.hstack([x, x0])

    # Sum Square Error
    predicted_Y = np.dot(np.dot(np.dot(X, np.linalg.pinv(np.dot(X.T, X))),
                                X.T), Y.flatten('F'))
    residuals = Y.flatten('F') - predicted_Y
    SSE = (residuals ** 2).sum()

    MSE = SSE / dfe

    # Sum square column effect - between colums
    SSC = ((np.mean(Y, 0) - mean_Y) ** 2).sum() * n
    MSC = SSC / dfc  # / n (without n in SPSS results)

    # Sum Square subject effect - between rows/subjects
    SSR = SST - SSC - SSE
    MSR = SSR / dfr

    if icc_type == 'icc1':
        # ICC(2,1) = (mean square subject - mean square error) /
        # (mean square subject + (k-1)*mean square error +
        # k*(mean square columns - mean square error)/n)
        # ICC = (MSR - MSRW) / (MSR + (k-1) * MSRW)
        NotImplementedError("This method isn't implemented yet.")

    elif icc_type == 'ICC(2,1)' or icc_type == 'ICC(2,k)':
        # ICC(2,1) = (mean square subject - mean square error) /
        # (mean square subject + (k-1)*mean square error +
        # k*(mean square columns - mean square error)/n)
        if icc_type == 'ICC(2,k)':
            k = 1
        ICC = (MSR - MSE) / (MSR + (k-1) * MSE + k * (MSC - MSE) / n)

    elif icc_type == 'ICC(3,1)' or icc_type == 'ICC(3,k)':
        # ICC(3,1) = (mean square subject - mean square error) /
        # (mean square subject + (k-1)*mean square error)
        if icc_type == 'ICC(3,k)':
            k = 1
        ICC = (MSR - MSE) / (MSR + (k-1) * MSE)

    return ICC