Model coding

Illustrates how to inspect coding of regression models.

# Author: Christian Brodbeck <christianbrodbeck@nyu.edu>
from eelbrain import *
from matplotlib import pyplot


ds = Dataset()
ds['A'] = Factor(['a1', 'a0'], repeat=4)
ds['B'] = Factor(['b1', 'b0'], repeat=2, tile=2)
ds.head()

A	B
a1	b1
a1	b1
a1	b0
a1	b0
a0	b1
a0	b1
a0	b0
a0	b0

Create a fixed effects model:

m = ds.eval('A * B')
m

A + B + A % B

Show the model using dummy coding:

m.as_table()

intercept	A	B	A x B
1	0	0	0
1	0	0	0
1	0	1	0
1	0	1	0
1	1	0	0
1	1	0	0
1	1	1	1
1	1	1	1

Create random effects model:

ds['subject'] = Factor(['s1', 's2'], tile=4, name='subject', random=True)
m = ds.eval('A * B * subject')
m

A + B + A % B + subject + A % subject + B % subject + A % B % subject

Show the model using dummy coding:

m.as_table()

intercept	A	B	A x B	subject	A x subject	B x subject	A x B x subject
1	0	0	0	1	0	0	0
1	0	0	0	0	0	0	0
1	0	1	0	1	0	1	0
1	0	1	0	0	0	0	0
1	1	0	0	1	1	0	0
1	1	0	0	0	0	0	0
1	1	1	1	1	1	1	1
1	1	1	1	0	0	0	0

Or with effect coding:

m.as_table('effect')

intercept	A	B	A x B	subject	A x subject	B x subject	A x B x subject
1	-1	-1	1	1	-1	-1	1
1	-1	-1	1	-1	1	1	-1
1	-1	1	-1	1	-1	1	-1
1	-1	1	-1	-1	1	-1	1
1	1	-1	-1	1	1	-1	-1
1	1	-1	-1	-1	-1	1	1
1	1	1	1	1	1	1	1
1	1	1	1	-1	-1	-1	-1

Plot model matrix:

figure, axes = pyplot.subplots(1, 2, figsize=(6, 3))
for ax, coding in zip(axes, ['dummy', 'effect']):
    array, names = m.array(coding)
    ax.imshow(array, cmap='coolwarm', vmin=-1, vmax=1)
    ax.set_title(coding)
    ax.set_xticks([i-0.5 for i in range(len(names))], names, rotation=-60, ha='left')