Quasi-likelihood specifies a mean and a variance function without necessarily specifying a full response distribution. For independent responses, the estimating equation is . A common scalar dispersion parameter rescales coefficient covariance while leaving the roots of the quasi-score equation unchanged.
Quasi-likelihood is a statistical framework used to estimate parameters in models where the likelihood function may not be fully specified or is difficult to derive. It extends the concept of likelihood by using a quasi-likelihood function that approximates the true likelihood of the observed data. The quasi-likelihood approach is particularly useful in situations where the distribution of the response variable is unknown or when the underlying data-generating process is complex.
New to topics? Read the docs here!