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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.
National lotteries : Games of chance held to heave money for particular causes. The first held in the UK took place in the year 1569 principally to raise money for repair of the Ci
Clinical vs. statistical significance : The distinction among results in terms of their possible clinical importance rather than simply in terms of their statistical importance. Wi
Last observation carried forward is a technique for replacing the observations of the patients who drop out of the clinical trial carried out over a time period. It consists of su
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Calibration : A procedure which enables a series of simply obtainable but inaccurate measurements of some quantity of interest to be used to provide more precise estimates of the r
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Random allocation is a technique for creating the treatment and control groups particularly in accordance of the clinical trial. Subjects receive the active treatment or the place
Over dispersion is the phenomenon which occurs when empirical variance in the data exceeds the nominal variance under some supposed model. Most often encountered when the modeling
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 >
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