algorithms.statistics.mixed_effects_stat¶
Module: algorithms.statistics.mixed_effects_stat¶
Inheritance diagram for nipy.algorithms.statistics.mixed_effects_stat:
Module for computation of mixed effects statistics with an EM algorithm. i.e. solves problems of the form y = X beta + e1 + e2, where X and Y are known, e1 and e2 are centered with diagonal covariance. V1 = var(e1) is known, and V2 = var(e2) = lambda identity. the code estimates beta and lambda using an EM algorithm. Likelihood ratio tests can then be used to test the columns of beta.
Author: Bertrand Thirion, 2012.
>>> N, P = 15, 500
>>> V1 = np.random.randn(N, P) ** 2
>>> effects = np.ones(P)
>>> Y = generate_data(np.ones(N), effects, .25, V1)
>>> T1 = one_sample_ttest(Y, V1, n_iter=5)
>>> T2 = t_stat(Y)
>>> assert(T1.std() < T2.std())
Class¶
MixedEffectsModel¶
-
class
nipy.algorithms.statistics.mixed_effects_stat.MixedEffectsModel(X, n_iter=5, verbose=False)[source]¶ Bases:
objectClass to handle multiple one-sample mixed effects models
-
__init__(X, n_iter=5, verbose=False)[source]¶ Set the effects and first-level variance, and initialize related quantities
- Parameters
X: array of shape(n_samples, n_effects),
the design matrix
n_iter: int, optional,
number of iterations of the EM algorithm
verbose: bool, optional, verbosity mode
-
log_like(Y, V1)[source]¶ Compute the log-likelihood of (Y, V1) under the model
- Parameters
Y, array of shape (n_samples, n_tests) or (n_samples)
the estimated effects
V1, array of shape (n_samples, n_tests) or (n_samples)
first-level variance
- Returns
logl: array of shape self.n_tests,
the log-likelihood of the model
-
Functions¶
-
nipy.algorithms.statistics.mixed_effects_stat.check_arrays(Y, V1)[source]¶ Check that the given data can be used for the models
- Parameters
Y: array of shape (n_samples, n_tests) or (n_samples)
the estimated effects
V1: array of shape (n_samples, n_tests) or (n_samples)
first-level variance
-
nipy.algorithms.statistics.mixed_effects_stat.generate_data(X, beta, V2, V1)[source]¶ Generate a group of individuals from the provided parameters
- Parameters
X: array of shape (n_samples, n_reg),
the design matrix of the model
beta: float or array of shape (n_reg, n_tests),
the associated effects
V2: float or array of shape (n_tests),
group variance
V1: array of shape(n_samples, n_tests),
the individual variances
- Returns
Y: array of shape(n_samples, n_tests)
the individual data related to the two-level normal model
-
nipy.algorithms.statistics.mixed_effects_stat.mfx_stat(Y, V1, X, column, n_iter=5, return_t=True, return_f=False, return_effect=False, return_var=False, verbose=False)[source]¶ Run a mixed-effects model test on the column of the design matrix
- Parameters
Y: array of shape (n_samples, n_tests)
the data
V1: array of shape (n_samples, n_tests)
first-level variance assocated with the data
X: array of shape(n_samples, n_regressors)
the design matrix of the model
column: int,
index of the column of X to be tested
n_iter: int, optional,
number of iterations of the EM algorithm
return_t: bool, optional,
should one return the t test (True by default)
return_f: bool, optional,
should one return the F test (False by default)
return_effect: bool, optional,
should one return the effect estimate (False by default)
return_var: bool, optional,
should one return the variance estimate (False by default)
verbose: bool, optional, verbosity mode
- Returns
(tstat, fstat, effect, var): tuple of arrays of shape (n_tests),
those required by the input return booleans
-
nipy.algorithms.statistics.mixed_effects_stat.one_sample_ftest(Y, V1, n_iter=5, verbose=False)[source]¶ Returns the mixed effects F-stat for each row of the X (one sample test) This uses the Formula in Roche et al., NeuroImage 2007
- Parameters
Y: array of shape (n_samples, n_tests)
the data
V1: array of shape (n_samples, n_tests)
first-level variance ssociated with the data
n_iter: int, optional,
number of iterations of the EM algorithm
verbose: bool, optional, verbosity mode
- Returns
fstat, array of shape (n_tests),
statistical values obtained from the likelihood ratio test
sign, array of shape (n_tests),
sign of the mean for each test (allow for post-hoc signed tests)
-
nipy.algorithms.statistics.mixed_effects_stat.one_sample_ttest(Y, V1, n_iter=5, verbose=False)[source]¶ Returns the mixed effects t-stat for each row of the X (one sample test) This uses the Formula in Roche et al., NeuroImage 2007
- Parameters
Y: array of shape (n_samples, n_tests)
the observations
V1: array of shape (n_samples, n_tests)
first-level variance associated with the observations
n_iter: int, optional,
number of iterations of the EM algorithm
verbose: bool, optional, verbosity mode
- Returns
tstat: array of shape (n_tests),
statistical values obtained from the likelihood ratio test
-
nipy.algorithms.statistics.mixed_effects_stat.t_stat(Y)[source]¶ Returns the t stat of the sample on each row of the matrix
- Parameters
Y, array of shape (n_samples, n_tests)
- Returns
t_variates, array of shape (n_tests)
-
nipy.algorithms.statistics.mixed_effects_stat.two_sample_ftest(Y, V1, group, n_iter=5, verbose=False)[source]¶ Returns the mixed effects t-stat for each row of the X (one sample test) This uses the Formula in Roche et al., NeuroImage 2007
- Parameters
Y: array of shape (n_samples, n_tests)
the data
V1: array of shape (n_samples, n_tests)
first-level variance assocated with the data
group: array of shape (n_samples)
a vector of indicators yielding the samples membership
n_iter: int, optional,
number of iterations of the EM algorithm
verbose: bool, optional, verbosity mode
- Returns
tstat: array of shape (n_tests),
statistical values obtained from the likelihood ratio test
-
nipy.algorithms.statistics.mixed_effects_stat.two_sample_ttest(Y, V1, group, n_iter=5, verbose=False)[source]¶ Returns the mixed effects t-stat for each row of the X (one sample test) This uses the Formula in Roche et al., NeuroImage 2007
- Parameters
Y: array of shape (n_samples, n_tests)
the data
V1: array of shape (n_samples, n_tests)
first-level variance assocated with the data
group: array of shape (n_samples)
a vector of indicators yielding the samples membership
n_iter: int, optional,
number of iterations of the EM algorithm
verbose: bool, optional, verbosity mode
- Returns
tstat: array of shape (n_tests),
statistical values obtained from the likelihood ratio test