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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: 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 >
The process of providing the numerical value for the population parameter on the basis of information gathered from a sample. If a single ?gure is computed for the unknown paramete
In the time series plot and scatter graphs there were many outliers that were clearly visible. These have been removed to identify if they were influential or had high leverage and
A test for equality of the variances of the two populations having normal distributions, based on the ratio of the variances of the sample of observations taken from each. Most fre
The Null Hypothesis - H0: β0 = 0, H0: β 1 = 0, H0: β 2 = 0, Β i = 0 The Alternative Hypothesis - H1: β0 ≠ 0, H0: β 1 ≠ 0, H0: β 2 ≠ 0, Β i ≠ 0 i =0, 1, 2, 3
Raking adjustments is an alternative to the post stratification adjustments in the complex surveys which ensures that the adjusted weights of the respondents conform to each of th
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
Quantalassay: The experiment in which the groups of subjects are exposed to the different doses of, generally, a drug, to which the particular number respond. Data from such type
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 regre
Graduation is the term is employed most often in the application of the actuarial statistics to denote procedures by which the set or group of observed probabilities is adjusted t
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