Modeling Count Data

taught by Joe Hilbe

Brief Description:

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. The course will cover Poisson regression, the foundation for modeling counts, as well as extensions and modifications to the basic model.

Instructor(s):
Level: Intermediate/Advanced

Who Should Take This Course:

Analysts and researchers in a wide variety of fields who are concerned with modeling counts and rates.

Dates:
October 19, 2012 to November 16, 2012
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Registration:
Please read the syllabus tab, noting the prerequisites, text and software requirements.

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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 is a core requirement or elective in the following Program(s) in Analytics and Statistical Studies (PASS):

• Biostatistics - Controlled Trials

• Biostatistics - Epidemiology

• Social Science

• Using R

Prerequisite(s):

Though it is not required for practical applications of material in this course, some familiarity with calculus (see statistics.com's brief Calculus Review course) is helpful for a complete understanding of model development.

Some familiarity with modeling - such as that provided in Regression Analysis or Logistic Regression will also be helpful. Categorical Data Analysis or its equivalent will also be helpful in acquainting participants with the type of data involved.

Course Program:

SESSION 1: Overview of Count Models and Methods of Estimation

• Varieties of count model
• History of count models
• Derivation of GLM-based algorithm
• Derivation of maximum likelihood count models
• Methods of assessing fit for count models
• Residual analysis
• The nature of risk and risk ratios

SESSION 2: Poisson Regression and the Problem of Overdispersion

• Poisson regression
• Creating synthetic models; simulation
• Predicting counts
• Effect plots
• Marginal effects/Discrete change
• Parameterization as a rate model
• Defining extra-dispersion: varieties
• Problem of overdispersion: apparent vs real
• Tests for handling overdispersion
• Negative  binomial extra-dispersion

SESSION 3: Negative Binomial Regression and Alternative Parameterizations

• Negative Binomial Regression: varieties, derivation, and distributions
• Synthetic data modeling
• Marginal effects/Discrete change: NB models
• Binomial vs Count models
• Geometric regression: canonical and log
• Alternative parameterizations: NB-1, NB-C, NB-H, NB-P
• Generalized Poisson and negative binomial models
• Extended Poisson models: bivariate; Poisson-inverse Gaussian; double Poisson
• Extended negative binomial models: bivariate; others

SESSION 4: Problem with Zero Counts; Censored and Truncated Models, Latent Models

• Zero-truncated models
• Zero-inflated models
• Zero-altered models
• Hurdle models
• Censored count models
• Finite Mixture models
• Quantile count models
• Exact Poisson and negative binomial regression
• 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.

Organization of the Course:

This course takes place over the internet at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

The course typically requires 15 hours per week. At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Credit:
Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

J. Hilbe's Negative Binomial Regression, 2nd edition (Cambridge Univ. Press). You can order it from Stata Press here or call 800-782-8272. It is available as an ebook here.

Software:

The methods covered in this course will be illustrated in both Stata and R. The majority of examples in the course text provide complete Stata code and output, but complete R code is also provided for all examples. All R data sets, functions and scripts used in the book are available in the COUNT package, that can be downloaded from CRAN. Stata code is provided on the publishers web site for the book. SAS and Excel data sets are provided as well.

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Modeling Count Data

taught by Joe Hilbe

Instructor(s):
Dates:
October 19, 2012 to November 16, 2012
Course Fee: $499
Academic Rate: $399

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