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)

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)

See LikelihoodModelResults constructor.

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

residuals()

Residuals from the fit.

normalized_residuals()

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()

Return linear predictor values from a design matrix.

SSE()

Error sum of squares. If not from an OLS model this is “pseudo”-SSE.

r_square()

Proportion of explained variance. If not from an OLS model this is “pseudo”-R2.

MSE()

Mean square (error)

Fcontrast(matrix, dispersion=None, invcov=None)

Compute an Fcontrast for a contrast matrix matrix.

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

M pX pX' M'

is assumed invertible. Here, 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)

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)

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()

The maximized log-likelihood

t(column=None)

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)

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.