Varieties of Count Data

Abstract

S ome P oints of D iscussion • What are counts? What are count data? • What is a linear statistical model? • What is the relationship between a probability distribution function (PDF) and a statistical model? • What are the parameters of a statistical model? Where do they come from, and can we ever truly know them? • How does a count model differ from other regression models? • What are the basic count models, and how do they relate with one another? • What is over dispersion, and why is it considered to be the fundamental problem when modeling count data? W hat A re C ounts ? When discussing the modeling of count data, it's important to clarify exactly what is meant by a count, as well as “count data” and “count variable.” The word “count” is typically used as a verb meaning to enumerate units, items, or events. We might count the number of road kills observed on a stretch of highway, how many patients died at a particular hospital within 48 hours of having a myocardial infarction, or how many separate sunspots were observed in March 2013. “Count data,” on the other hand, is a plural noun referring to observations made about events or items that are enumerated. In statistics, count data refer to observations that have only nonnegative integer values ranging from zero to some greater undetermined value. Theoretically, counts can range from zero to infinity, but they are always limited to some lesser distinct value – generally the maximum value of the count data being modeled.