Dear Dmitrii Petrukhin
In (20.2), the authors are talking about unconditional distributions, not regression; a regression is always about a conditional distribution. If you are doing regression, then you specify mu as in (20.3) and equidispersion is then defined as the equality between the conditional mean and conditional variance. If your goal it is just to estimate mu; overdispersion can safely be ignored if you use robust standard errors (see the discussion on page 670).
Best wishes,
Joao
In (20.2), the authors are talking about unconditional distributions, not regression; a regression is always about a conditional distribution. If you are doing regression, then you specify mu as in (20.3) and equidispersion is then defined as the equality between the conditional mean and conditional variance. If your goal it is just to estimate mu; overdispersion can safely be ignored if you use robust standard errors (see the discussion on page 670).
Best wishes,
Joao
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