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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.
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The Null Hypothesis - H0: There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1: There is heteroscedasticity i.e. β 1 0 Reject H0 if Q = ESS/2 >
Principal components regression analysis is a process often taken in use to overcome the problem of multicollinearity in the regression, when simply deleting a number of the expla
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Window variables are the variables measured during the constrained interval of an observation period which is accepted as the proxies for the information over the whole period. Fo
The division of a sample of observations into several classes, together with the number of observations in each of them. It acts as a useful summary of the main features of the da
Demographic data: Age: continuous variable Gender: categorical variable with males coded 1, females coded 2. Relationship status: categorical variable 1 to 5. Rational
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