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# Predicting Count Data - PowerPoint PPT Presentation

Predicting Count Data. Poisson Regression. Review: Confusing Statistical Terms. General Linear Model (GLM) -Anything that can be written like this: -Solved using ordinary least squares -Assumptions revolve around the Normal Dist. Generalized Linear Model

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Predicting Count Data

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## Predicting Count Data

Poisson Regression

### Review: Confusing Statistical Terms

General Linear Model (GLM)

-Anything that can be written like this:

-Solved using ordinary least squares

-Assumptions revolve around the Normal Dist.

Generalized Linear Model

-Anything that can be written like this:

-Solved using maximum likelihood

-Assumptions use many different distributions

### Remember: Why These Models?

• Linear Regression: Assuming normal errors around the predicted score

• When we violate this assumptions, our estimates of the distributions of the B’s are incorrect

• Also…in some case our estimates of the effect size are inaccurate (usually too small)

### Linear Regression

• Linear regression is really a predictive model before anything else. (The statistical aspect is extra).

B1

B0

### Examples

• (Criminal Justice) Number of offenses per year

• (Domestic Violence) Number of DV events per person

• (Epidemiology) Number of seizures per week

### Count Data

• This type of data can only have discrete values that are greater than or equal to zero.

• In situations, this data follows the Poisson Distribution

### Poisson Distribution

• The Poisson random variable is defined by one parameter: the mean (μ)

• It has the strong assumption that the mean is equal to the variance

μ=σ

### Poisson Regression

• In this model, instead of predicting mean of a normal distribution, you are predicting the mean of a Poisson distribution (given some predictors)

### Fundamental Equation

• In linear regression:

• In Poisson regression:

### Assumptions

• In your outcome variable (Y), the mean equals the variance. (There is a test for this)

• For violations you can use Negative Binomial…which is just a Poisson where the variance is separate from the mean.

• Observations are independent (as with most analyses)

• And, basically, that the predictive model makes sense ( )

### Interpreting Parameters

• Like logistic, we have to interpret the EXP(B)

• (This is the notation for )

• Instead of an odds ratio, this is a relative risk ratio: it is the additional rate given a one unit increase in X

• 1 is the null hypothesis

• 1.2 would be an increase of .2 in the relative rate for a one unit increase

### Really, why the trouble?

• Turns out that not using Poisson isn’t the worst thing ever.

• Actually get alpha deflation

• BUT- Many journals that are used to this kind of data will reject articles that do not use the proper technique