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Binomial.deviance()

statsmodels.genmod.families.family.Binomial.deviance

Binomial.deviance(endog, mu, freq_weights=1, scale=1.0) [source]

Deviance function for either Bernoulli or Binomial data.

Parameters:

Parameters:	endog : array-like Endogenous response variable (already transformed to a probability if appropriate). mu : array Fitted mean response variable freq_weights : array-like 1d array of frequency weights. The default is 1. scale : float, optional An optional scale argument. The default is 1.
Returns:	deviance : float The deviance function as defined below

endog : array-like

Endogenous response variable (already transformed to a probability if appropriate).

mu : array

Fitted mean response variable

freq_weights : array-like

1d array of frequency weights. The default is 1.

scale : float, optional

An optional scale argument. The default is 1.

Returns:

deviance : float

The deviance function as defined below

Notes

If the endogenous variable is binary:

$D = -2 * \sum_i freq\_weights * (I_{1,i} * \log(\mu_i) + I_{0,i} * \log(1 - \mu_i))$

where $I_{1,i}$ is an indicator function that evalueates to 1 if $Y_i = 1$ . and $I_{0,i}$ is an indicator function that evaluates to 1 if $Y_i = 0$ .

If the model is ninomial:

$D = 2 * \sum_i freq\_weights * (\log(Y_i / \mu_i) + (n_i - Y_i) * \log((n_i - Y_i) / n_i - \mu_i))$

where $Y_i$ and $n$ are as defined in Binomial.initialize.

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.genmod.families.family.Binomial.deviance.html