generalized linear models

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

Member Training: Confusing Statistical Terms

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Learning statistics is difficult enough; throw in some especially confusing terminology and it can feel impossible! There are many ways that statistical language can be confusing.

Some terms mean one thing in the English language, but have another (usually more specific) meaning in statistics. [Read more…] about Member Training: Confusing Statistical Terms

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…]

Member Training: The Multi-Faceted World of Residuals

by Karen Grace-Martin 1 Comment

Most analysts’ primary focus is to check the distributional assumptions with regards to residuals. They must be independent and identically distributed (i.i.d.) with a mean of zero and constant variance.

Residuals can also give us insight into the quality of our models.

In this webinar, we’ll review and compare what residuals are in linear regression, ANOVA, and generalized linear models. Jeff will cover:

Which residuals — standardized, studentized, Pearson, deviance, etc. — we use and why
How to determine if distributional assumptions have been met
How to use graphs to discover issues like non-linearity, omitted variables, and heteroskedasticity

Knowing how to piece this information together will improve your statistical modeling skills.

Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

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: