1.2.14. patsy.Poly¶

class patsy.Poly(scores=None)[source]¶

Orthogonal polynomial contrast coding.

This coding scheme treats the levels as ordered samples from an underlying continuous scale, whose effect takes an unknown functional form which is Taylor-decomposed into the sum of a linear, quadratic, etc. components.

For reduced-rank coding, you get a linear column, a quadratic column, etc., up to the number of levels provided.

For full-rank coding, the same scheme is used, except that the zero-order constant polynomial is also included. I.e., you get an intercept column included as part of your categorical term.

By default the levels are treated as equally spaced, but you can override this by providing a value for the scores argument.

Examples:

# Reduced rank
In [1]: dmatrix("C(a, Poly)", balanced(a=4))
Out[1]: 
DesignMatrix with shape (4, 4)
  Intercept  C(a, Poly).Linear  C(a, Poly).Quadratic  C(a, Poly).Cubic
          1           -0.67082                   0.5          -0.22361
          1           -0.22361                  -0.5           0.67082
          1            0.22361                  -0.5          -0.67082
          1            0.67082                   0.5           0.22361
  Terms:
    'Intercept' (column 0)
    'C(a, Poly)' (columns 1:4)

# Full rank
In [2]: dmatrix("0 + C(a, Poly)", balanced(a=3))
Out[2]: 
DesignMatrix with shape (3, 3)
  C(a, Poly).Constant  C(a, Poly).Linear  C(a, Poly).Quadratic
                    1           -0.70711               0.40825
                    1           -0.00000              -0.81650
                    1            0.70711               0.40825
  Terms:
    'C(a, Poly)' (columns 0:3)

# Explicit scores
In [3]: dmatrix("C(a, Poly([1, 2, 10]))", balanced(a=3))
Out[3]: 
DesignMatrix with shape (3, 3)
  Intercept  C(a, Poly([1, 2, 10])).Linear  C(a, Poly([1, 2, 10])).Quadratic
          1                       -0.47782                           0.66208
          1                       -0.33447                          -0.74485
          1                        0.81229                           0.08276
  Terms:
    'Intercept' (column 0)
    'C(a, Poly([1, 2, 10]))' (columns 1:3)

This is equivalent to R’s contr.poly. (But note that in R, reduced rank encodings are always dummy-coded, regardless of what contrast you have set.)

__init__(scores=None)[source]¶