y = c(2,3,6,7,8,9,10,12,15)
x = c(-1, -1, 0, 0, 0, 0, 1, 1, 1)

glm(y~x, family = poisson)

lf = sum(y * log(y) - y - log(factorial(y)))
ln = sum(y * log(mean(y)) - mean(y) - log(factorial(y)))

2*(lf - ln)

glm(y~x - 1, family = poisson)

glm(y~1-1, family=poisson)