Modeling Count Data Guideline

Syllabus Requirements Dates Register

Modeling Count Data
taught by Joe Hilbe

Aim of Course:This course 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 Poisson regression, the foundation for modeling counts, as well as extensions and modifications to the basic model. Extensions are required when the assumptions underlying the Poisson model are violated. Negative binomial regression is the foremost method used to extend the Poisson model. Since Poisson assumptions are rarely met in practice, substantial attention will be devoted to the negative binomial model and its variants.
This course may be taken individually (one-off) or as part of a certificate program.
Course Program:

WEEK 1: Fundamentals of Modeling Counts; the Basic Poisson model

• What are counts
• History of count models
• Risk and risk ratios
• Understanding  statistical count models
• Variety of count models
• Estimation - the modeling process
• Poisson model assumptions
• The basic Poisson model

WEEK 2: Poisson Regression and the Problem of Overdispersion

• Simulation and creation of synthetic count models
• Poisson regression -- Interpreting Poisson coefficients
• Modeling incidence and rate ratios
• Modeling counts over time, area or space
• Predicting counts and probability
• Marginal effects/Discrete change
• Problem of overdispersion: what is overdispersion
• Apparent vs real overdispersion - how to tell
• Tests for handling overdispersion
• Assessment of Fit -- residuals, likelihood ratio test, AIC/BIC, etc

WEEK 3: Negative Binomial Regression and Alternative Parameterizations

• Negative Binomial Regression: varieties, derivation, and distributions
• Marginal effects/Discrete change: NB models
• General negative binomial fit tests
• Heterogeneous negative binomial  (NBH)
• Generalized Poisson - modeling underdispersion  (GP)
• Poisson inverse Gaussian (PIG)
• Generalized NB-P regression (NBP)
• Problem of zeros  - zero-truncated models (ZTP, ZTNB, ZTPIG, ZTGP, ZTNBP, etc)

WEEK 4: Problem with Zero Counts; more advanced models

• Two-part hurdle models
• Zero-inflated mixture models  (ZIP, ZINB, ZIPIG, ZIGP, ZINBP, etc))
• Exact Poisson regression
• Truncation and censored count models
• Finite mixture models
• Non-parametric and quantile count models
• Overview of longitudinal models
• 3-parameter count models
• Overview of Bayesian count models
• Project preparation

HOMEWORK:
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.