The COUNTREG Procedure
- Overview
- Getting Started
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Syntax
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Details
Specification of Regressors Missing Values Poisson Regression Negative Binomial Regression Zero-Inflated Count Regression Overview Zero-Inflated Poisson Regression Zero-Inflated Negative Binomial Regression Computational Resources Nonlinear Optimization Options Covariance Matrix Types Displayed Output OUTPUT OUT= Data Set OUTEST= Data Set ODS Table Names
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Examples
- References
| Zero-Inflated Poisson Regression |
In the zero-inflated Poisson (ZIP) regression model, the data generation process referred to earlier as Process 2 is
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where 
. Thus the ZIP model is defined as
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The conditional expectation and conditional variance of 
are given by
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Note that the ZIP model (as well as the ZINB model) exhibits overdispersion since 
.
In general, the log-likelihood function of the ZIP model is
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After a specific link function (either logistic or standard normal) for the probability 
is chosen, it is possible to write the exact expressions for the log-likelihood function and the gradient.
ZIP Model with Logistic Link Function
First, consider the ZIP model in which the probability is expressed with a logistic link function—namely,
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The log-likelihood function is
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See Poisson Regression for the definition of 
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The gradient for this model is given by
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ZIP Model with Standard Normal Link Function
Next, consider the ZIP model in which the probability is expressed with a standard normal link function: 
. The log-likelihood function is
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See Poisson Regression for the definition of .
The gradient for this model is given by
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