C29. Saturated model and deviance

Topic: Paired comparisons, and how far a fit is from the data · more questions on this topic
‹ C26 C30 ›

What is a saturated model, and what does deviance compare? Distinguish deviance from scaled deviance.

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Definitions/notation. A saturated mean model fits each observed response exactly (\tilde\mu_i=y_i, possibly as a boundary limit); at common dispersion \phi, the scaled deviance is D/\phi=2\{\ell(\tilde\mu;y,\phi)-\ell(\hat\mu;y,\phi)\}. Thus the unscaled deviance D is \phi times that log-likelihood-ratio discrepancy, and equals the scaled deviance when \phi=1.