Modeling Count Data

Modeling Count Data

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taught by James Hardin

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Aim of Course:

This online course, "Modeling Count Data" deals with regression models for count data; i.e. models with a response or dependent variable data in the form of a count or rate. A count is understood as the number of times an event occurs; a rate as how many events occur within a specific area or time interval. The course will cover the nature of count models, Poisson regression, negative binomial regression, problems of over- and under-dispersion, fit and residual tests and graphics for count models, problems with zeros (zero truncated and zero inflated mixture models, two-part hurdle models), and advanced models such as Poisson inverse Gaussian (PIG), generalized Poisson and generalized negative binomial models, left, right and interval truncated and censored count models, finite mixture models, quantile count models, generalized additive modeling, handling longitudinal and clustered count data, mixture count models, and an overview of Bayesian count models.  

This course may be taken individually (one-off) or as part of a certificate program.
Course Program:

WEEK 1: Fundamentals of Modeling Counts; Poisson Regression

  • What are counts
  • Understanding a statistical count model
  • Variety of count models
  • Estimation - the modeling process
  • Poisson model assumptions
  • Apparent overdispersion
  • The basic Poisson mode
  • Interpreting coefficients and rate ratios
  • Exposure; modeling time, area, and space
  • Prediction
  • Poisson marginal effects

WEEK 2: Overdispersion, Assessment of Fit, and Negative Binomial Regression

  • Count  model fit statistics
  • Overdispersion: what, why, and how
  • Testing overdispersion
  • Methods for handling overdispersion – adjusting SEs
  • Analysis of residuals
  • Likelihood ratio tests
  • Model selection criterion
  • Validation sample
  • Varieties of negative binomial models
  • Negative binomial model assumptions
  • Examples using real data


WEEK 3: Alternative Count Models: NB Fit tests, PIG, Problem with Zeros

  • General negative binomial fit tests
  • Generalized NB-P regression (NBP)
  • Heterogeneous negative binomial  (NBH)
  • Generalized Poisson - modeling underdispersion  (GP)
  • Poisson inverse Gaussian (PIG)
  • Zero-truncated count models
  • Two-part hurdle models
  • Zero-inflated count models

WEEK 4: Underdispersed count data, Advanced count models

  • Generalized Poisson – modeling underdispersion
  • Exact Poisson regression
  • Truncation and censored count models
  • Finite mixture models
  • Non-parametric and quantile count models
  • Overview of longitudinal and clustered count models
  • 3-parameter count models
  • Overview of Bayesian count models
  • Project preparation


Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, guided data modeling problems using software and end of course data modeling project. In addition to assigned readings, this course also has supplemental readings available online in the course.

Note:  The Institute gratefully acknowledges the contribution of Prof. Joseph Hilbe, the original developer and instructor for the course.

Modeling Count Data

Who Should Take This Course:
Analysts and researchers in a wide variety of fields who are concerned with modeling counts and rates.
Some familiarity with linear modeling - such as that provided in Regression Analysis will be helpful.
Organization of the Course:
Options for Credit and Recognition:
Course Text:

The required text is Modeling Count Data, Hilbe, Joseph M (2014), Cambridge University Press. This paperback edition includes R, Stata, SAS and Excel/CVS code, which can be downloaded from the author’s website. R data and functions are located in the COUNT package on CRAN. An electronic version of the book is also available from the publisher, or on Amazon.


The methods covered in this course are handled well by Stata, R and for the most part, SAS.  Data sets used in the text are available in Stata, R SAS and Excel formats.   With respect to code and output:

Stata:  Code and output are provided for all examples for which known Stata commands exist.

R:  Functions and scripts are available in the COUNT and msme packages; additional R code is provided at the following web site: Most examples have R support.

SAS:  Some code and output is provided (e.g. chapter 15 on Bayesian count models).

The instructor and TA are familiar with Stata and R.  The instructor is familiar with most SAS procedures related to the modeling of count data. No instructional support is available for SAS.  If you plan on using R and are not already familiar with it, please consider taking one of our courses where R is introduced from the ground up:  R-Programming: Introduction," "Introduction to R: Data Handling," or "Introduction to R: Statistical Analysis."  R has a learning curve that is steeper than that of most commercial statistical software.



October 25, 2019 to November 22, 2019 October 23, 2020 to November 20, 2020

Modeling Count Data


October 25, 2019 to November 22, 2019 October 23, 2020 to November 20, 2020

Course Fee: $589

Do you meet course prerequisites? What about book & software? (Click here to learn more)

We have flexible policies to transfer to another course, or withdraw if necessary (modest fee applies)

Group rates: Click here to get information on group rates. 

First time student or academic? Click here for an introductory offer on select courses. Academic affiliation?  You may be eligible for a discount at checkout.

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