C28. Dispersion

Topic: Underdispersion, positive responses, and quasi-likelihood · more questions on this topic
‹ C27

What is the dispersion parameter \phi in \operatorname{Var}(Y_i\mid x_i)=\phi V(\mu_i)? Define overdispersion and underdispersion relative to \phi=1.

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Definitions/notation. In \operatorname{Var}(Y_i\mid x_i)=\phi V(\mu_i), the function V specifies the variance’s dependence on the mean and the positive scalar \phi scales that variance. Relative to the baseline \phi=1, overdispersion means \phi>1 and underdispersion means 0<\phi<1; for quasi-Poisson, V(\mu)=\mu.