def isestimable(C, D):
"""
From an q x p contrast matrix C and an n x p design matrix D, checks
if the contrast C is estimable by looking at the rank of vstack([C,D]) and
verifying it is the same as the rank of D.
"""
if C.ndim == 1:
C.shape = (C.shape[0], 1)
new = np.vstack([C, D])
if matrix_rank(new) != matrix_rank(D):
return False
return True
def initialize(self, design):
# PLEASE don't assume we have a constant...
# TODO: handle case for noconstant regression
self.design = design
self.wdesign = self.whiten(self.design)
self.calc_beta = spl.pinv(self.wdesign)
self.normalized_cov_beta = np.dot(self.calc_beta,
np.transpose(self.calc_beta))
self.df_total = self.wdesign.shape[0]
self.df_model = matrix_rank(self.design)
self.df_resid = self.df_total - self.df_model
def isestimable(C, D):
""" True if (Q, P) contrast `C` is estimable for (N, P) design `D`
From an Q x P contrast matrix `C` and an N x P design matrix `D`, checks if
the contrast `C` is estimable by looking at the rank of ``vstack([C,D])``
and verifying it is the same as the rank of `D`.
Parameters
----------
C : (Q, P) array-like
contrast matrix. If `C` has is 1 dimensional assume shape (1, P)
D: (N, P) array-like
design matrix
Returns
-------
tf : bool
True if the contrast `C` is estimable on design `D`
Examples
--------
>>> D = np.array([[1, 1, 1, 0, 0, 0],
... [0, 0, 0, 1, 1, 1],
... [1, 1, 1, 1, 1, 1]]).T
>>> isestimable([1, 0, 0], D)
False
>>> isestimable([1, -1, 0], D)
True
"""
C = np.asarray(C)
D = np.asarray(D)
if C.ndim == 1:
C = C[None, :]
if C.shape[1] != D.shape[1]:
raise ValueError('Contrast should have %d columns' % D.shape[1])
new = np.vstack([C, D])
if matrix_rank(new) != matrix_rank(D):
return False
return True
def rank(self):
""" Compute rank of design matrix
"""
return matrix_rank(self.wdesign)
def contrast_from_cols_or_rows(L, D, pseudo=None):
""" Construct a contrast matrix from a design matrix D
(possibly with its pseudo inverse already computed)
and a matrix L that either specifies something in
the column space of D or the row space of D.
Parameters
----------
L : ndarray
Matrix used to try and construct a contrast.
D : ndarray
Design matrix used to create the contrast.
pseudo : None or array-like, optional
If not None, gives pseudo-inverse of `D`. Allows you to pass
this if it is already calculated.
Returns
-------
C : ndarray
Matrix with C.shape[1] == D.shape[1] representing an estimable
contrast.
Notes
-----
From an n x p design matrix D and a matrix L, tries to determine a p
x q contrast matrix C which determines a contrast of full rank,
i.e. the n x q matrix
dot(transpose(C), pinv(D))
is full rank.
L must satisfy either L.shape[0] == n or L.shape[1] == p.
If L.shape[0] == n, then L is thought of as representing
columns in the column space of D.
If L.shape[1] == p, then L is thought of as what is known
as a contrast matrix. In this case, this function returns an estimable
contrast corresponding to the dot(D, L.T)
This always produces a meaningful contrast, not always
with the intended properties because q is always non-zero unless
L is identically 0. That is, it produces a contrast that spans
the column space of L (after projection onto the column space of D).
"""
L = np.asarray(L)
D = np.asarray(D)
n, p = D.shape
if L.shape[0] != n and L.shape[1] != p:
raise ValueError('shape of L and D mismatched')
if pseudo is None:
pseudo = pinv(D)
if L.shape[0] == n:
C = np.dot(pseudo, L).T
else:
C = np.dot(pseudo, np.dot(D, L.T)).T
Lp = np.dot(D, C.T)
if len(Lp.shape) == 1:
Lp.shape = (n, 1)
Lp_rank = matrix_rank(Lp)
if Lp_rank != Lp.shape[1]:
Lp = full_rank(Lp, Lp_rank)
C = np.dot(pseudo, Lp).T
return np.squeeze(C)
def contrast_from_cols_or_rows(L, D, pseudo=None):
""" Construct a contrast matrix from a design matrix D
(possibly with its pseudo inverse already computed)
and a matrix L that either specifies something in
the column space of D or the row space of D.
Parameters
----------
L : ndarray
Matrix used to try and construct a contrast.
D : ndarray
Design matrix used to create the contrast.
pseudo : None or array-like, optional
If not None, gives pseudo-inverse of `D`. Allows you to pass
this if it is already calculated.
Returns
-------
C : ndarray
Matrix with C.shape[1] == D.shape[1] representing an estimable
contrast.
Notes
-----
From an n x p design matrix D and a matrix L, tries to determine a p
x q contrast matrix C which determines a contrast of full rank,
i.e. the n x q matrix
dot(transpose(C), pinv(D))
is full rank.
L must satisfy either L.shape[0] == n or L.shape[1] == p.
If L.shape[0] == n, then L is thought of as representing
columns in the column space of D.
If L.shape[1] == p, then L is thought of as what is known
as a contrast matrix. In this case, this function returns an estimable
contrast corresponding to the dot(D, L.T)
This always produces a meaningful contrast, not always
with the intended properties because q is always non-zero unless
L is identically 0. That is, it produces a contrast that spans
the column space of L (after projection onto the column space of D).
"""
L = np.asarray(L)
D = np.asarray(D)
n, p = D.shape
if L.shape[0] != n and L.shape[1] != p:
raise ValueError('shape of L and D mismatched')
if pseudo is None:
pseudo = pinv(D)
if L.shape[0] == n:
C = np.dot(pseudo, L).T
else:
C = np.dot(pseudo, np.dot(D, L.T)).T
Lp = np.dot(D, C.T)
if len(Lp.shape) == 1:
Lp.shape = (n, 1)
Lp_rank = matrix_rank(Lp)
if Lp_rank != Lp.shape[1]:
Lp = full_rank(Lp, Lp_rank)
C = np.dot(pseudo, Lp).T
return np.squeeze(C)