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Results tagged with Search options user 111259
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Deviance is twice the difference between the maximum achievable log likelihood and that attained under the fitted model.

Is there an integral form of the deviance residual? I've always seen the deviance residual written as $$d_i = 2w_i\Big(y_i\big(\tilde{\theta}_i - \hat{\theta}_i\big) - \big(b(\tilde{\theta}_i) - b … (\hat{\theta}_i)\big) \Big)$$ While studying for an actuarial exam, I've run into the deviance residual in the following form d_i = 2w_i \int_{\mu_i}^{y_i} \dfrac{y_i - \xi}{\operatorname{Var …
I've been studying some GLM theory, and I ran into deviance recently. Seems like the deviance has properties similar to a metric. Namely: $D(y, y)=0$ Non-negativity $D(y, \mu) \geq 0$ I … hesitate to add subadditivity to the list, but Deviance has something like it. Furthermore, when we fit a GLM, we maximize the log liklihood function, which in turn should minimize the deviance, no? So does deviance have an interpretation as a distance? …