# gamma glm to dgamma

I am modelling the average claim amount (claim amount/number of claims), so i used a gamma glm with weights=number of claims, as:

> model<-glm(claimamount/numclaims ~ 1 + veh_age + zone + insured_age,
> family=Gamma(link = "log"), weights = numclaims)


After this i want to find the log likelihood at each observation, but glm only return the sum, for instances:

> logLik(model)
>'log Lik.' -70665.26


How can i get the loglikelihood for each observation?

I tried to do:

> x<-claimamount/numclaims
> m<-model.matrix(model)       # covariates
> mu<-as.vector(exp(m%*%coef(model)))    #mean
> delta<-summary(model)$dispersion # dispersion parameter > ll<-log(dgamma(x,1/delta,1/(delta*mu)))  But when i sum all the loglikelihoods(to check if it is ok), i don't get the same value as in logLik(model). My question is: what am i doing wrong? is it because i used weights in glm and i also have to use the weights in dgamma? • You will need to show us the details of what you're doing if you would like us to identify what is going wrong. If the call to dgamma literally is what you have computed, then evidently you need to take its logarithm using the log=TRUE argument. – whuber Jul 18 '17 at 12:50 • @whuber i hope that it is more understandable now – maria Jul 18 '17 at 18:58 • It is, thank you. Are you sure you have the arguments to dgamma correct? – whuber Jul 18 '17 at 20:37 • @whuber it is correct when there is no weights, according to the glm/gamma parameterization... but i am not sure if it is the same when we have weights, it is one of my questions – maria Jul 19 '17 at 0:31 ## 1 Answer The problem, as you noticed yourself, is that you use weights for your model, while you are not using them in your by-hand calculations. If you check the source of logLik.glm, you'll see that it uses AIC to calculate back the log likelihood: p <- object$rank
## allow for estimated dispersion
if(fam %in% c("gaussian", "Gamma", "inverse.gaussian")) p <- p + 1
val <- p - object\$aic / 2


Now compare the Gamma source to check how AIC is calculated:

dev.resids <- function(y, mu, wt)
-2 * wt * (log(ifelse(y == 0, 1, y/mu)) - (y - mu)/mu)
aic <- function(y, n, mu, wt, dev){
n <- sum(wt)
disp <- dev/n
-2*sum(dgamma(y, 1/disp, scale=mu*disp, log=TRUE)*wt) + 2


it uses weighted deviance to calculate it. In fact, for weighted data we use weighted likelihood (see example here)