Note

This page is a reference documentation. It only explains the class signature, and not how to use it. Please refer to the user guide for the big picture.

nilearn.glm.RegressionResults#

class nilearn.glm.RegressionResults(theta, Y, model, whitened_Y, whitened_residuals, cov=None, dispersion=1.0, nuisance=None)[source]#

This class summarizes the fit of a linear regression model.

It handles the output of contrasts, estimates of covariance, etc.

Notes

This class is experimental. It may change in any future release of Nilearn.

__init__(theta, Y, model, whitened_Y, whitened_residuals, cov=None, dispersion=1.0, nuisance=None)[source]#

See LikelihoodModelResults constructor.

The only difference is that the whitened Y and residual values are stored for a regression model.

residuals()[source]#: Residuals from the fit.

normalized_residuals()[source]#

Residuals, normalized to have unit length.

See 1 and 2.

Notes

Is this supposed to return “stanardized residuals,” residuals standardized to have mean zero and approximately unit variance?

d_i = e_i / sqrt(MS_E)

Where MS_E = SSE / (n - k)

References

1: Douglas C. Montgomery, Elizabeth A. Peck, and Geoffrey G. Vining. Introduction to Linear Regression Analysis (4th ed.). Wiley & Sons, 2006. ISBN 0471754951.
2: Russell Davidson and James G. MacKinnon. Econometric theory and methods. Oxford Univ. Press, New York, NY [u.a.], 2004. ISBN 978-0-19-512372-2. URL: http://gso.gbv.de/DB=2.1/CMD?ACT=SRCHA&SRT=YOP&IKT=1016&TRM=ppn+393847152&sourceid=fbw_bibsonomy.

predicted()[source]#: Return linear predictor values from a design matrix.

SSE()[source]#: Error sum of squares. If not from an OLS model this is “pseudo”-SSE.

r_square()[source]#: Proportion of explained variance. If not from an OLS model this is “pseudo”-R2.

MSE()[source]#: Mean square (error)

Fcontrast(matrix, dispersion=None, invcov=None)[source]#

Compute an Fcontrast for a contrast matrix matrix.

Here, matrix M is assumed to be non-singular. More precisely

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is assumed invertible. Here,

System Message: WARNING/2 (pX)

is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full.

See the contrast module to see how to specify contrasts. In particular, the matrices from these contrasts will always be non-singular in the sense above.

Parameters

matrix1D array-like: Contrast matrix.
dispersionNone or float, optional: If None, use self.dispersion.
invcovNone or array, optional: Known inverse of variance covariance matrix. If None, calculate this matrix.

Returns

f_resFContrastResults instance: with attributes F, df_den, df_num

Notes

For F contrasts, we now specify an effect and covariance.

Tcontrast(matrix, store=('t', 'effect', 'sd'), dispersion=None)[source]#

Compute a Tcontrast for a row vector matrix

To get the t-statistic for a single column, use the ‘t’ method.

Parameters

matrix1D array-like: Contrast matrix.
storesequence, optional: Components of t to store in results output object. Defaults to all components (‘t’, ‘effect’, ‘sd’).
dispersionNone or float, optional

Returns

resTContrastResults object

conf_int(alpha=0.05, cols=None, dispersion=None)[source]#

The confidence interval of the specified theta estimates.

Parameters

alphafloat, optional: The alpha level for the confidence interval. ie., alpha = .05 returns a 95% confidence interval. Default=0.05.
colstuple, optional: cols specifies which confidence intervals to return.
dispersionNone or scalar, optional: Scale factor for the variance / covariance (see class docstring and vcov method docstring).

Returns

cisndarray: cis is shape (len(cols), 2) where each row contains [lower, upper] for the given entry in cols

Notes

Confidence intervals are two-tailed.

tailsstring, optional: Possible values: ‘two’ | ‘upper’ | ‘lower’

Examples

>>> from numpy.random import standard_normal as stan
>>> from nilearn.glm import OLSModel
>>> x = np.hstack((stan((30,1)),stan((30,1)),stan((30,1))))
>>> beta=np.array([3.25, 1.5, 7.0])
>>> y = np.dot(x,beta) + stan((30))
>>> model = OLSModel(x).fit(y)
>>> confidence_intervals = model.conf_int(cols=(1,2))

logL()[source]#: The maximized log-likelihood

t(column=None)[source]#

Return the (Wald) t-statistic for a given parameter estimate.

Use Tcontrast for more complicated (Wald) t-statistics.

vcov(matrix=None, column=None, dispersion=None, other=None)[source]#

Variance/covariance matrix of linear contrast

Parameters

matrix(dim, self.theta.shape[0]) array, optional: Numerical contrast specification, where dim refers to the ‘dimension’ of the contrast i.e. 1 for t contrasts, 1 or more for F contrasts.
columnint, optional: Alternative way of specifying contrasts (column index).
dispersionfloat or (n_voxels,) array, optional: Value(s) for the dispersion parameters.
other(dim, self.theta.shape[0]) array, optional: Alternative contrast specification (?).

Returns

cov(dim, dim) or (n_voxels, dim, dim) array: The estimated covariance matrix/matrices.
Returns the variance/covariance matrix of a linear contrast of the
estimates of theta, multiplied by dispersion which will often be an
estimate of dispersion, like, sigma^2.
The covariance of interest is either specified as a (set of) column(s)
or a matrix.