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Poisson regression
In case of Poisson regression we use ηi = g(µi) = log(µi) and a variance V ar(Yi) = φµi. The case φ = 1 corresponds to standard Poisson model. Poisson regression is used when the response to model is counts which typically follow a Poisson distribution. Examples include colony counts for bacteria or viruses, accidents, equipment failures, insurance claims, incidence of disease. Interest often lies in estimating a rate of incidence and determining its relationship to a set of explanatory variables. Again, an IRLS procedure is used to ?nd the MLE estimators of the β coeffcients. When we can not assume φ = 1, (this is the case of over- or under- dispersion discussed in McCullagh and Nelder (1989)), the iterative procedure is changed to so called "quasi-likelihood estimation". Finally in this section, we shall also mention shortly the extension of GLM to GAM.
The Null Hypothesis - H0: Model does not fit the data i.e. all slopes are equal to zero β 1 =β 2 =...=β k = 0 The Alternative Hypothesis - H1: Model does fit the data i.e. at
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Observational study is the study in which the objective is to discover cause-and-effect relationships but in which it is not feasible to use the controlled experimentation, in th
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