What happens to the variance-covariance matrix when implementing the quasi-likelihood method?

What happens to the variance-covariance matrix when implementing the quasi-likelihood method?

• A. It remains unchanged.
• B. It is inverted.
• C. It is scaled by a dispersion parameter.
• D. It is scaled by adding an extra parameter to reflect data variability.

Answer: (D)

In quasi-likelihood you don’t pin down a full distribution for the data; instead you combine a mean model with a variance function and include a dispersion parameter to capture extra variability. The key is that the variability of Y given its mean is Var(Y|μ) = φ V(μ), where φ is the dispersion parameter. This φ acts as an extra scale factor for the variance, so the variance-covariance matrix of the estimated coefficients is scaled by φ. In practical terms, this means the standard errors are inflated or deflated by roughly sqrt(φ) to reflect overdispersion or underdispersion in the data.

In quasi-likelihood you don’t pin down a full distribution for the data; instead you combine a mean model with a variance function and include a dispersion parameter to capture extra variability. The key is that the variability of Y given its mean is Var(Y|μ) = φ V(μ), where φ is the dispersion parameter. This φ acts as an extra scale factor for the variance, so the variance-covariance matrix of the estimated coefficients is scaled by φ. In practical terms, this means the standard errors are inflated or deflated by roughly sqrt(φ) to reflect overdispersion or underdispersion in the data.