Massive univariate linear model.
Linear models for massive univariate statistics.
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class
mulm.models.MUOLS(Y, X)[source]¶ Mass-univariate linear modeling based Ordinary Least Squares. Given two arrays X (n_samples, p) and Y (n_samples, q). Fit q independent linear models, ie., for all y in Y fit: lm(y ~ X).
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f_test(contrast, pval=False)[source]¶ - Compute F-statistics (F-scores and p-value associated to contrast).
The code has been cloned from the SPM MATLAB implementation.
- Parameters
contrasts: array (q, ) or list of arrays or array 2D.
Single contrast (array) or list of contrasts or array of contrasts. The k contrasts to be tested.
pval: boolean
compute pvalues (default is false)
two_tailed: boolean
one-tailed test or a two-tailed test (default True)
- Returns
tstats (k, p) array, pvals (k, p) array, df (k,) array
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fit(block=False, max_elements=134217728)[source]¶ Fit p independent linear models, ie., for all y in Y fit: lm(y ~ X).
- Parameters
block : boolean
Use block=True for huge matrices Y. Operations block by block to optimize time and memory.
max_elements : int
block dimension (2**27 corresponds to 1Go)
- Returns
self
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predict(X)[source]¶ Predict Y given a new design matrix X.
- Parameters
X : numpy array (n_samples, q)
design matrix of new predictors.
- Returns
(n_samples, 1) array of predicted values (X beta)
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t_test(contrasts, pval=False, two_tailed=True)[source]¶ - Compute T-statistics (t-scores and p-value associated to contrast).
The code has been cloned from the SPM MATLAB implementation.
- Parameters
contrasts: array (q, ) or list of arrays or array 2D.
Single contrast (array) or list of contrasts or array of contrasts. The k contrasts to be tested.
pval: boolean
compute pvalues (default is false)
two_tailed: boolean
one-tailed test or a two-tailed test (default True)
- Returns
tstats (k, p) array, pvals (k, p) array, df (k,) array
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t_test_maxT(contrasts, nperms=1000, two_tailed=True, **kwargs)[source]¶ - Correct for multiple comparisons using Westfall and Young, 1993 a.k.a maxT procedure.
It is based on permutation tests procedure. This is the procedure used by FSL (https://fsl.fmrib.ox.ac.uk/).
It should be used when the test statistics, and hence the unadjusted p-values, are dependent. This is the case when groups of dependant variables (in Y) tend to have highly correlated measures. Westfall and Young (1993) proposed adjusted p-values for less conservative multiple testing procedures which take into account the dependence structure among test statistics. References: - Anderson M. Winkler “Statistical analysis of areal quantities in the brain through permutation tests” Ph.D 2017. - Dudoit et al. “Multiple Hypothesis Testing in Microarray Experiments”, Statist. Sci. 2003
- Parameters
contrasts: array (q, ) or list of arrays or array 2D.
Single contrast (array) or list of contrasts or array of contrasts. The k contrasts to be tested.
nperms: int
permutation tests (default 1000).
two_tailed: boolean
one-tailed test or a two-tailed test (default True)
- Returns
tstats (k, p) array, pvals (k, p) array corrected for multiple comparisons
df (k,) array.
Examples
>>> import numpy as np >>> import mulm >>> np.random.seed(42) >>> # n_samples, nb of features that depends on X and that are pure noise >>> n_samples, n_info, n_noise = 100, 2, 100 >>> beta = np.array([1, 0, 0.5, 0, 2])[:, np.newaxis] >>> X = np.random.randn(n_samples, 5) # Design matrix >>> X[:, -1] = 1 # Intercept >>> Y = np.random.randn(n_samples, n_info + n_noise) >>> Y[:, :n_info] += np.dot(X, beta) # n_info features depend from X >>> contrasts = np.identity(X.shape[1])[:4] # don't test the intercept >>> mod = mulm.MUOLS(Y, X).fit() >>> tvals, pvals, df = mod.t_test(contrasts, two_tailed=True) >>> print(pvals.shape) (4, 102) >>> print("Nb of uncorrected p-values <5%:", np.sum(pvals < 0.05)) Nb of uncorrected p-values <5%: 18 >>> tvals, pvals_corrmaxT, df = mod.t_test_maxT(contrasts, two_tailed=True) >>> print("Nb of corrected pvalues <5%:", np.sum(pvals_corrmaxT < 0.05)) Nb of corrected pvalues <5%: 4
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t_test_minP(contrasts, nperms=10000, two_tailed=True, **kwargs)[source]¶ Correct for multiple comparisons using minP procedure.
References: - Dudoit et al. “Multiple Hypothesis Testing in Microarray Experiments”, Statist. Sci. 2003
- Parameters
contrasts: array (q, ) or list of arrays or array 2D.
Single contrast (array) or list of contrasts or array of contrasts. The k contrasts to be tested.
nperms: int
permutation tests (default 10000).
two_tailed: boolean
one-tailed test or a two-tailed test (default True)
- Returns
tstats (k, p) array, pvals (k, p) array corrected for multiple comparisons
df (k,) array.
Examples
>>> import numpy as np >>> import mulm >>> np.random.seed(42) >>> # n_samples, nb of features that depends on X and that are pure noise >>> n_samples, n_info, n_noise = 100, 2, 100 >>> beta = np.array([1, 0, 0.5, 0, 2])[:, np.newaxis] >>> X = np.random.randn(n_samples, 5) # Design matrix >>> X[:, -1] = 1 # Intercept >>> Y = np.random.randn(n_samples, n_info + n_noise) >>> Y[:, :n_info] += np.dot(X, beta) # n_info features depend from X >>> contrasts = np.identity(X.shape[1])[:4] # don't test the intercept >>> mod = mulm.MUOLS(Y, X).fit() >>> tvals, pvals, df = mod.t_test(contrasts, two_tailed=True) >>> print(pvals.shape) (4, 102) >>> print("Nb of uncorrected p-values <5%:", np.sum(pvals < 0.05)) Nb of uncorrected p-values <5%: 18 >>> tvals, pval_corrminp, df = mod.t_test_minP(contrasts, two_tailed=True) >>> print("Nb of corrected pvalues <5%:", np.sum(pval_corrminp < 0.05)) Nb of corrected pvalues <5%: 4
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class
mulm.models.MUPairwiseCorr(X, Y)[source]¶ Mass-univariate pairwise correlations. Given two arrays X (n_samples x p) and Y (n_samples x q). Fit p x q independent linear models. Prediction and stats return (p x q) array.
Examples
>>> import numpy as np >>> from mulm import MUPairwiseCorr >>> X = np.random.randn(10, 5) >>> Y = np.random.randn(10, 3) >>> corr = MUPairwiseCorr(X, Y) >>> corr.fit() <mulm.models.MUPairwiseCorr instance at 0x30da878> >>> f, p = corr.stats_f() >>> print(f.shape) (5, 3)
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