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Concept
Zero-inflated model
Summary
In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued observations.
Zero-inflated models are commonly used in the analysis of count data, such as the number of visits a patient makes to the emergency room in one year, or the number of fish caught in one day in one lake. Count data can take values of 0, 1, 2, ... (non-negative integer values). Other examples of count data are the number of hits recorded by a Geiger counter in one minute, patient days in the hospital, goals scored in a soccer game, and the number of episodes of hypoglycemia per year for a patient with diabetes.
For statistical analysis, the distribution of the counts is often represented using a Poisson distribution or a negative binomial distribution. Hilbe notes that "Poisson regression is traditionally conceived of as the basic count model upon which a variety of other count models are based." In a Poisson model, "... the random variable is the count response and parameter (lambda) is the mean. Often, is also called the rate or intensity parameter... In statistical literature, is also expressed as (mu) when referring to Poisson and traditional negative binomial models."
In some data, the number of zeros is greater than would be expected using a Poisson distribution or a negative binomial distribution. Data with such an excess of zero counts are described as Zero-inflated.
Example histograms of zero-inflated Poisson distributions with mean of 5 or 10 and proportion of zero inflation of 0.2 or 0.5 are shown below, based on the R program ZeroInflPoiDistPlots.R from Bilder and Laughlin.
Fish counts "... suppose we recorded the number of fish caught on various lakes in 4-hour fishing trips to Minnesota. Some lakes in Minnesota are too shallow for fish to survive the winter, so fishing in those lakes will yield no catch. On the other hand, even on a lake where fish are plentiful, we may or may not catch any fish due to conditions or our own competence.
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