R Programming/Count Data Models

Count data The Poisson model Poisson regression 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 Markus Jochmann (2010). zic: Bayesian Inference for Zero-Inflated Count Models. R package version 0.5-3. http://CRAN.R-project.org/package=zic 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 bookCameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press. are provided in the AER packageChristian Kleiber and Achim Zeileis (2008). Applied Econometrics with R. New York: Springer-Verlag. ISBN 978-0-387-77316-2. URL http://CRAN.R-project.org/package=AER. You can simply type ?CameronTrivedi1998 and you will find the source code. 2