Poisson regression Analysis

Poisson regression Analysis

1. It is a regression technique available for modeling dependent variables that describe count (i.e., discrete) datal

   • Objective
     • To discuss the Poisson regression model and several key features of the model, particularly how a rate ratio (RR) can be estimated using Poisson regression
       • The Poisson Distribution
         • The Poisson distribution is often used to model the occurrence of rare events
           • number of new cases of lung cancer in period of time
             • Breast cancer in men (a notably rare disease)
               • Variance of Poisson Distribution are equal
                 • Over-dispersion
                   • variances are either larger than sample means
                 • “under-dispersion”
                   • or smaller than sample means
           • “typical” Poisson regression model,
             • the natural measures of effect that are estimated are rate ratios.
       • ML estimation
         • It is used to estimate the regression coefficients of a Poisson regression model.
           • The likelihood function for Poisson regression analysis is of the general form
             • The likelihood function assumes that the underlying response (a count) has the Poisson distribution.
               • LR test for Poisson regression can be carried out equivalently by using differences in deviance statistics.
       • Measures of Goodness of Fit
         • is obtained by using the deviance statistic, which is an LR-type statistic reflecting the fit of a current model of interest relative to the baseline (uninformative or “saturated”) model (which involves as many parameters as there are data points).
       • Poisson ANOVA table
         • A summary of the results of fitting various models to the data set under consideration can be presented in a Poisson ANOVA table

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