Types of Poisson Regression

Offset Regression A variant of Poisson Regression Count data often have an exposure variable, which indicates the number of times the event could have happened This variable should be incorporated into a Poisson model with the use of the offset option

Offset Regression If all the students have same exposure to math (program), the number of awards are comparable But if there is variation in the exposure, it could affect the count A count of 5 awards out of 5 years is much bigger than a count of 1 out of 3 Rate of awards is count/exposure In a model for awards count, the exposure is moved to the right side Then if the algorithm of count is logged & also the exposure, the final model contains ln(exposure) as term that is added to the regression equation This logged variable, ln(exposure) or a similarity constructed variable is called the offset variable

Offset Poisson Regression A data frame with 63 observations on the following 4 variables. (lung.cancer) years.smok a factor giving the number of years smoking cigarettes a factor giving cigarette consumption Time man-years at risk y number of deaths

Negative Binomial Regression One potential drawback of Poisson regression is that it may not accurately describe the variability of the counts A Poisson distribution is parameterized by λ, which happens to be both its mean and variance. While convenient to remember, it’s not often realistic. A distribution of counts will usually have a variance that’s not equal to its mean. When we see this happen with data that we assume (or hope) is Poisson distributed, we say we have under- or over dispersion, depending on if the variance is smaller or larger than the mean. Performing Poisson regression on count data that exhibits this behavior results in a model that doesn’t fit well.

One approach that addresses this issue is Negative Binomial Regression. We go for Negative Binomial Regression when Variance > Mean (over dispersion)

The negative binomial distribution, like the Poisson distribution, describes the probabilities of the occurrence of whole numbers greater than or equal to 0. The variance of a negative binomial distribution is a function of its mean and has an additional parameter, k, called the dispersion parameter. The variance of a negative binomial distribution is a function of its mean and has an additional parameter, k, called the dispersion parameter. var(Y)=μ+μ2/k

Zero Inflated Regression

ExcelR is considered as the best Data Science training institute in Chennai which offers services from training to placement as part of the...

Published on May 16, 2019

ExcelR is considered as the best Data Science training institute in Chennai which offers services from training to placement as part of the...

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