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.
- class nilearn.glm.ARModel(design, rho)[source]#
A regression model with an AR(p) covariance structure.
In terms of a LikelihoodModel, the parameters are beta, the usual regression parameters, and sigma, a scalar nuisance parameter that shows up as multiplier in front of the AR(p) covariance.
- __init__(design, rho)[source]#
Initialize AR model instance.
2D array with design matrix.
- rhoint or array-like
If int, gives order of model, and initializes rho to zeros. If ndarray, gives initial estimate of rho. Be careful as
ARModel(X, 1) != ARModel(X, 1.0).
Whiten a series of columns according to AR(p) covariance structure.
- Xarray-like of shape (n_features)
Array to whiten.
X whitened with order self.order AR.
Fit model to data Y.
Full fit of the model including estimate of covariance matrix, (whitened) residuals and scale.
The dependent variable for the Least Squares problem.
- logL(beta, Y, nuisance=None)[source]#
Return the value of the loglikelihood function at beta.
Given the whitened design matrix, the loglikelihood is evaluated at the parameter vector, beta, for the dependent variable, Y and the nuisance parameter, sigma .
The parameter estimates. Must be of length df_model.
The dependent variable
- nuisancedict, optional
A dict with key ‘sigma’, which is an optional estimate of sigma. If None, defaults to its maximum likelihood estimate (with beta fixed) as
sum((Y - X*beta)**2) / n, where n=Y.shape, X=self.design.
The value of the loglikelihood function.
The log-Likelihood Function is defined as
The parameter above is what is sometimes referred to as a nuisance parameter. That is, the likelihood is considered as a function of , but to evaluate it, a value of is needed.
If is not provided, then its maximum likelihood estimate:
is plugged in. This likelihood is now a function of only and is technically referred to as a profile-likelihood.