ExcelR

1. Types of Poisson Regression

2. 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

3. 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

4. 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

5. 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.

6.  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

7. Zero Inflated Regression