I have a question about quasi-likelihood. I think the following formula says something opposite to what likelihood means. Could someone clarify what I'm misunderstanding.
I'm looking at the formula in the page of variance function in Wikipedia .
I think this formula says, when the $\mu_i$ and $y_i$ are closer, $Q_i$ becomes smaller. The reason I think like this is that the range of integral is defined by $\mu_i$ and $y_i$, and when they are closer, the range is narrower.
However, this formula represents a kind of likelihood, quasi-likelihood, so my intuition says that when the $\mu_i$ is closer to $y_i$ , quasi-likelihood should be larger, because this situation should be more likely. I'm comparing quasi-likelihood with usual likelihood (used in maximum likelihood). In maximum likelihoods situation, when the observed value and mean are closer, the likelihood is larger.
Could someone clarify the point I'm misunderstanding. Thank you!
P.S. I'm not a math guy and my approach is applied statistics. So easy math explanation is preferable!