= Null deviance
{title2=$D_0=2\phi[\ell_{\rm saturated}-\ell_{\rm intercept}]$}
The <null deviance> is the unscaled <deviance> of the intercept-only mean model relative to the saturated model at a common <dispersion parameter> $\phi$, retaining any known <generalized linear model offset>. It supplies a baseline against which predictor terms improve the fit. Its difference from a fitted model's <residual deviance>, divided by $\phi$, is the statistic for a <likelihood-ratio test> of those added terms, with nuisance parameters handled consistently in both fits. In Poisson and binomial families, $\phi=1$.
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