Data Analytics Courses.

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