Poisson Regression

Interactions in statistical models are never especially easy to interpret. Throw in non-normal outcome variables and non-linear prediction functions and they become even more difficult to understand. (more…)

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When your dependent variable is not continuous, unbounded, and measured on an interval or ratio scale, linear models don’t fit. The data just will not meet the assumptions of linear models. But there’s good news, other models exist for many types of dependent variables.

Today I’m going to go into more detail about 6 common types of dependent variables that are either discrete, bounded, or measured on a nominal or ordinal scale and the tests that work for them instead. Some are all of these.

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Even if you’ve never heard the term Generalized Linear Model, you may have run one. It’s a term for a family of models that includes logistic and Poisson regression, among others.

It’s a small leap to generalized linear models, if you already understand linear models. Many, many concepts are the same in both types of models.

But one thing that’s perplexing to many is why generalized linear models have no error term, like linear models do. (more…)

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When our outcome variable is the frequency of occurrence of an event, we will typically use a count model to analyze the results. There are numerous count models. A few examples are: Poisson, negative binomial, zero-inflated Poisson and truncated negative binomial.

There are specific requirements for which count model to use. The models are not interchangeable. But regardless of the model we use, there is a very important prerequisite that they all share.

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When we run a statistical model, we are in a sense creating a mathematical equation. The simplest regression model looks like this:

Y_i = β₀ + β₁X+ ε_i

The left side of the equation is the sum of two parts on the right: the fixed component, β₀ + β₁X, and the random component, ε_i.

You’ll also sometimes see the equation written (more…)

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Generalized linear models—and generalized linear mixed models—are called generalized linear because they connect a model’s outcome to its predictors in a linear way. The function used to make this connection is called a link function. Link functions sounds like an exotic term, but they’re actually much simpler than they sound.

For example, Poisson regression (commonly used for outcomes that are counts) makes use of a natural log link function as follows:

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