pydiodon.bicentering

pydiodon.bicentering(A)

Bicentering a matrix

Parameters:

Aa n x p numpy array

the matrix to be bicentered

Returns:

ma float

global mean of the matrix

ra 1D numpy array (n values)

rowise means

ca 1D numpy arrau (p values)

columnwise means

Ra 2D numpy array (n x p)

bicentered matrix

Notes

If A is a matrix, builds a matrix R of same dimension centered on rows and columns.

\(m = (1/np) \sum_{i,j} a_{ij}\)

\(r = (r_1,...,r_n)\) with \(r_i = (1/p)\sum_j a_{ij} - m\)

\(c = (c_1,...,c_p)\) with \(c_j = (1/n)\sum_i a_{ij} - m\)

such that

\(\sum_ir_i = \sum_jc_j=0\)

and

for any row i, \(\sum_j R_{ij}=0\) and for any column j, \(\sum_i R_{ij}=0\)

The matrix R can describe interactions in a additive model with two categorical variables, as in

\(a_{ij} = m + r_i + c_j + R_{ij}\)

example

>>> import pydiodon as dio
>>> import numpy as np
>>> n = 4 ; p = 3
>>> A = np.arange(n*p)
>>> A.shape=(n,p)
>>> m, r, c, R = dio.bicenter(A)

af, revised 21.02.19, 22.09.21, 22.10.13