Poisson/Negative Binomial

Question 1

Poisson Regression

Answer 1

Fundamental distribution used for count data and contingency tables. Poisson regression is appropriate for rate data where the rate is a count of events divided by some measure of that unit’s exposure.

Question 2

Offset Term

Answer 2

Included in formula which is usually represented by the exposure amounts for each observation

Question 3

Equidispersion

Answer 3

The mean of Y equals the variance of Y. The larger one is the larger the other will be

Question 4

What does the log of the poisson formula do?

Answer 4

The log of this will ensure a linear combination and force all the mean values to be non-negative, which makes sense for a lot of our models

Question 5

Negative Binomial Regression

Answer 5

Based on a Poisson-Gamma mixture distribution, which models the Poisson heterogeneity with a Gamma distribution, allowing for the mean and variance to differ.

Question 6

How do we fit a negative binomial regression model to a count dependent variable?

Answer 6

We let a parameter p vary by observation i

Question 7

Pearson Chi-Square Statistic

Answer 7

Examines regression models for count dependent variables. This is just an actual vs. expected analysis to help us identify how well our model predicts. Between the Chi-squared for two models, the lower stat would identify the best model.