Inheritance diagram for nipy.algorithms.statistics.models.glm:
Bases: nipy.algorithms.statistics.models.regression.WLSModel
Methods
cont | |
deviance | |
estimate_scale | |
fit | |
has_intercept | |
information | |
initialize | |
logL | |
next | |
predict | |
rank | |
score | |
whiten |
Continue iterating, or has convergence been obtained?
Return (unnormalized) log-likelihood for GLM.
Note that self.scale is interpreted as a variance in old_model, so we divide the residuals by its sqrt.
Return Pearson’s X^2 estimate of scale.
Check if column of 1s is in column space of design
Returns the information matrix at (beta, Y, nuisance).
See logL for details.
Parameters : | beta : ndarray
nuisance : dict
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Returns : | info : array
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Returns 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.
Parameters : | beta : ndarray
Y : ndarray
nuisance : dict, optional
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Returns : | loglf : float
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Notes
The log-Likelihood Function is defined as .. math:
\ell(\beta,\sigma,Y)=
-\frac{n}{2}\log(2\pi\sigma^2) - \|Y-X\beta\|^2/(2\sigma^2)
The parameter \sigma above is what is sometimes referred to as a nuisance parameter. That is, the likelihood is considered as a function of \beta, but to evaluate it, a value of \sigma is xneeded.
If \sigma is not provided, then its maximum likelihood estimate:
\hat{\sigma}(\beta) = \frac{\text{SSE}(\beta)}{n}
is plugged in. This likelihood is now a function of only \beta and is technically referred to as a profile-likelihood.
References
[R1] |
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After a model has been fit, results are (assumed to be) stored in self.results, which itself should have a predict method.
Compute rank of design matrix
Returns the score function, the gradient of the loglikelihood function at (beta, Y, nuisance).
See logL for details.
Parameters : | beta : ndarray
Y : ndarray
nuisance : dict, optional
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Returns : | The gradient of the loglikelihood function. : |
Whitener for WLS model, multiplies by sqrt(self.weights)