R Programming/Count Data Models

The Poisson model

Fake data simulations

We assume that y follows a poisson distribution with mean exp(1 + 1 * x). We store the data in the "df" dataframe.

N <- 1000
x <- rnorm(N)
alpha <- c(1,1)
y <- rpois(N,exp(alpha[1] + alpha[2] * x))
df <- data.frame(x,y)
plot(x,y)

Maximum likelihood

We estimate this simple model using the glm() function with family = poisson as option.

fit <- glm(y ~ x, family = poisson, data = df)
summary(fit)

Bayesian estimation

The model can also be estimated using bayesian methods with the MCMCpoisson() function which is provided in the MCMCpack.

library("MCMCpack")
posterior <- MCMCpoisson(y ~ x, data = df)
plot(posterior)
summary(posterior)

Overdispersion test

• dispersiontest() (AER package) provides a test for equidispersion.

Zero inflated model

See the zic package

Bivariate poisson regression

• bivpois package for bivariate poisson regression.

References

• See UCLA website for an example
• Zeileis, A., Kleiber, C. and Jackman, S. Regression Models for Count Data in R
• Replication files for Cameron and Trivedi's 1998 book are provided in the AER package. You can simply type ?CameronTrivedi1998 and you will find the source code.