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m →Types of variance functions: typo |
Disambiguated: score function → scoring rule (2) |
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: – Variance function: <math>V(\mu)\text{, where the }\operatorname{Var}_\theta(y) = \sigma^2V(\mu)</math>
With a specified variance function and link function we can develop, as alternatives to the log-[[likelihood function]], the [[scoring rule|score function]], and the [[Fisher information]], a '''[[quasi-likelihood]]''', a '''quasi-score''', and the '''quasi-information'''. This allows for full inference of <math>\beta</math>.
'''Quasi-likelihood (QL)'''
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'''Quasi-score (QS)'''
Recall the [[scoring rule|score function]], '''U''', for data with log-likelihood <math>\operatorname{l}(\mu\mid y)</math> is
:<math>U = \frac{\partial l }{d\mu}.</math>
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