Inheritance diagram for nipy.algorithms.statistics.models.glm:
Bases: nipy.algorithms.statistics.models.regression.WLSModel
Methods
cont([tol]) | Continue iterating, or has convergence been obtained? |
deviance([Y, results, scale]) | Return (unnormalized) log-likelihood for GLM. |
estimate_scale([Y, results]) | Return Pearson’s X^2 estimate of scale. |
fit(Y) | |
has_intercept() | Check if column of 1s is in column space of design |
information(beta[, nuisance]) | Returns the information matrix at (beta, Y, nuisance). |
initialize(design) | |
logL(beta, Y[, nuisance]) | Returns the value of the loglikelihood function at beta. |
next() | |
predict([design]) | After a model has been fit, results are (assumed to be) stored |
rank() | Compute rank of design matrix |
score(beta, Y[, nuisance]) | Gradient of the loglikelihood function at (beta, Y, nuisance). |
whiten(X) | Whitener for WLS model, multiplies by sqrt(self.weights) |
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
\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 needed.
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
Gradient of the loglikelihood function at (beta, Y, nuisance).
The graient of the loglikelihood function at (beta, Y, nuisance) is the score function.
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)