When we run a statistical model, we are in a sense creating a mathematical equation. The simplest regression model looks like this:
Yi = β0 + β1X+ εi
The left side of the equation is the sum of two parts on the right: the fixed component, β0 + β1X, and the random component, εi.
You’ll also sometimes see the equation written (more…)
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:
Transformations don’t always help, but when they do, they can improve your linear regression model in several ways simultaneously.
They can help you better meet the linear regression assumptions of normality and homoscedascity (i.e., equal variances). They also can help avoid some of the artifacts caused by boundary limits in your dependent variable — and sometimes even remove a difficult-to-interpret interaction.
Ah, logarithms. They were frustrating enough back in high school. (If you even got that far in high school math.)
And they haven’t improved with age, now that you can barely remember what you learned in high school.
And yet… they show up so often in data analysis.
If you don’t quite remember what they are and how they work, they can make the statistical methods that use them seem that much more obtuse.
So we’re going to take away that fog of confusion about exponents and logs and how they work. (more…)