link function

Count Models: Understanding the Log Link Function

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 [Read more…] about Count Models: Understanding the Log Link Function

How to Decide Between Multinomial and Ordinal Logistic Regression Models

by Karen Grace-Martin 6 Comments

A great tool to have in your statistical tool belt is logistic regression.

It comes in many varieties and many of us are familiar with the variety for binary outcomes.

But multinomial and ordinal varieties of logistic regression are also incredibly useful and worth knowing.

They can be tricky to decide between in practice, however. In some — but not all — situations you [Read more…] about How to Decide Between Multinomial and Ordinal Logistic Regression Models

The Difference Between Link Functions and Data Transformations

by Kim Love 1 Comment

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:

Member Training: Generalized Linear Models

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In this webinar, we will provide an overview of generalized linear models. You may already be using them (perhaps without knowing it!).

For example, logistic regression is a type of generalized linear model that many people are already familiar with. Alternatively, maybe you’re not using them yet and you are just beginning to understand when they might be useful to you.

[Read more…]

Link Functions and Errors in Logistic Regression

by Karen Grace-Martin 1 Comment

I recently held a free webinar in our The Craft of Statistical Analysis program about Binary, Ordinal, and Nominal Logistic Regression.

It was a record crowd and we didn’t get through everyone’s questions, so I’m answering some here on the site. They’re grouped by topic, and you will probably get more out of it if you watch the webinar recording. It’s free.

The following questions refer to this logistic regression model: [Read more…] about Link Functions and Errors in Logistic Regression

The Difference Between Logistic and Probit Regression

by Karen Grace-Martin 12 Comments

One question that seems to come up pretty often is:

What is the difference between logistic and probit regression?

Well, let’s start with how they’re the same:

Both are types of generalized linear models. This means they have this form: