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

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Predicting Count Data

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Predicting count data

Predicting Count Data

Poisson Regression


Review confusing statistical terms

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

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

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

B1

B0


Count data

Count Data


Examples

Examples

  • (Criminal Justice) Number of offenses per year

  • (Domestic Violence) Number of DV events per person

  • (Epidemiology) Number of seizures per week


Count data1

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

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

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

Fundamental Equation

  • In linear regression:

  • In Poisson regression:


Assumptions

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

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

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


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