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)¶ Bases:
object
Class to handle multiple one-sample mixed effects models
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__init__
(X, n_iter=5, verbose=False)¶ 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
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fit
(Y, V1)¶ Launches the EM algorithm to estimate self
- 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
- self
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log_like
(Y, V1)¶ 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
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predict
(Y, V1)¶ Return the log_likelihood of the data.See the log_like method
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score
(Y, V1)¶ Return the log_likelihood of the data. See the log_like method
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Functions¶
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nipy.algorithms.statistics.mixed_effects_stat.
check_arrays
(Y, V1)¶ 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
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nipy.algorithms.statistics.mixed_effects_stat.
generate_data
(X, beta, V2, V1)¶ 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
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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)¶ 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
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nipy.algorithms.statistics.mixed_effects_stat.
one_sample_ftest
(Y, V1, n_iter=5, verbose=False)¶ 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)
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nipy.algorithms.statistics.mixed_effects_stat.
one_sample_ttest
(Y, V1, n_iter=5, verbose=False)¶ 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
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nipy.algorithms.statistics.mixed_effects_stat.
t_stat
(Y)¶ 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)
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nipy.algorithms.statistics.mixed_effects_stat.
two_sample_ftest
(Y, V1, group, n_iter=5, verbose=False)¶ 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
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nipy.algorithms.statistics.mixed_effects_stat.
two_sample_ttest
(Y, V1, group, n_iter=5, verbose=False)¶ 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