Poisson deviance simplifies when an intercept is fitted
= Poisson deviance simplifies when an intercept is fitted
{c}
{title2=$D=2\sum_i y_i\log(y_i/e_i)$}
The full <Poisson deviance> is $2\sum_i[y_i\log(y_i/e_i)-y_i+e_i]$. An unpenalized log-mean intercept has <likelihood> score $\sum_i(y_i-e_i)$, which vanishes at an interior fit. The linear terms then cancel, giving the displayed expression. Without that intercept score equation, discarding the linear terms is not justified. Use the limiting convention $0\log(0/e_i)=0$.