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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.
Bartlett's test for variances : A test for equality of the variances of the number (k)of the populations. The test statistic can be given as follows where s square is an
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Remedian: The robust estimator of location which is computed by an iterative process. By assuming that the sample size n can be written as bk where b and k are the integers, the s
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Wilcoxon's ranksum test is the distribution free method or technique used as an alternative to the Student's t-test for assessing whether two populations have the same location. G
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Cluster randomization : The random allocation of the groups or clusters of the individuals in the formation of treatment groups.Eeven though not as statistically ef?cient as the in
The phrase first spoken by one of the witches in Macbeth. Now this is used to describe the exponential rise in the number of possible locations in the multivariate space as dimensi
A family of the probability distributions of the form given as here θ is the parameter and a, b, c, d are the known functions. It includes the gamma distribution, normal dis
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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