Poisson Regression is a statistical method used for modeling and predicting the frequency of events in various fields. It assumes a Poisson distribution of count data, where the mean equals the variance. The technique is ideal for analyzing event occurrences and is adaptable through methods like Negative Binomial Regression or Zero Inflated Poisson Regression to handle overdispersion and excess zeros.
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Poisson Regression is a predictive modeling technique for count data that assumes a Poisson distribution
Equidispersion
Poisson Regression assumes that the mean and variance of the data are equal, known as equidispersion
Log-linear relationship
The model assumes a log-linear relationship between the expected count and the independent variables
The data must meet certain criteria, including being count data, independent, and following a Poisson distribution, for the model to be valid
Poisson Regression is useful for predicting the frequency of events in various fields, such as public health and transportation
The model can examine the impact of changes in predictor variables on the incidence rate of an event
Poisson Regression is widely used in fields like public health, transportation, and actuarial science
Overdispersion, where the variance of the data exceeds the mean, can be a challenge for the basic Poisson model
Negative Binomial Regression
When overdispersion occurs, alternative models like Negative Binomial Regression can be used
Zero Inflated Poisson Regression (ZIP)
For datasets with a high number of zero counts, ZIP offers an enhancement to the standard Poisson model
The regression coefficients in Poisson Regression reflect a multiplicative effect on the event rate, not a direct additive effect on the counts
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In ______ Regression, the expected number of event occurrences is assumed to follow a distribution where the mean equals the variance.
Poisson
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Poisson Regression Assumption
Assumes count data are independent and follow Poisson distribution, implying equidispersion.
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Poisson vs. Overdispersion
Poisson Regression unsuitable for overdispersion where variance exceeds mean; Negative Binomial Regression or offset variable may be used.
