LLq n a i0 y ilogsq Tx 1 y log1 sq x We will show the derivation later. The log-likelihood function is typically used to derive the maximum likelihood estimator of the parameter. If we drop the term not involving th to be justithed later we obtain logLth 1 2s2 Xn i1 xi th2.
Take the log of the likelihood equation the result is.
For the gaussian Gamma and inversegaussian families it assumed that the dispersion of the GLM is estimated has been counted as a parameter in the AIC value and for all other families it is assumed that the dispersion is known. Displaystyle theta is the likelihood function given the outcome. The log likelihood ie the log of the likelihood will always be negative with higher values closer to zero indicating a better fitting model. Lets call them th_mu and th_sigma.