Mixed and Multilevel Models

Regression Diagnostics in Generalized Linear Mixed Models

What are the best methods for checking a generalized linear mixed model (GLMM) for proper fit?

This question comes up frequently.

Unfortunately, it isn’t as straightforward as it is for a general linear model.

In linear models the requirements are easy to outline: linear in the parameters, normally distributed and independent residuals, and homogeneity of variance (that is, similar variance at all values of all predictors).

Eight Ways to Detect Multicollinearity

by Karen Grace-Martin 5 Comments

Multicollinearity can affect any regression model with more than one predictor. It occurs when two or more predictor variables overlap so much in what they measure that their effects are indistinguishable.

When the model tries to estimate their unique effects, it goes wonky (yes, that’s a technical term).

So for example, you may be interested in understanding the separate effects of altitude and temperature on the growth of a certain species of mountain tree.

The Difference Between Random Factors and Random Effects

by Karen Grace-Martin 6 Comments

Mixed models are hard.

They’re abstract, they’re a little weird, and there is not a common vocabulary or notation for them.

But they’re also extremely important to understand because many data sets require their use.

Repeated measures ANOVA has too many limitations. It just doesn’t cut it any more.

One of the most difficult parts of fitting mixed models is figuring out which random effects to include in a model. And that’s hard to do if you don’t really understand what a random effect is or how it differs from a fixed effect. [Read more…] about The Difference Between Random Factors and Random Effects

Member Training: Latent Growth Curve Models

by Jeff Meyer 2 Comments

What statistical model would you use for longitudinal data to analyze between-subject differences with within-subject change?

Most analysts would respond, “a mixed model,” but have you ever heard of latent growth curves? How about latent trajectories, latent curves, growth curves, or time paths, which are other names for the same approach?

[Read more…]

Understanding Random Effects in Mixed Models

by Kim Love 2 Comments

In fixed-effects models (e.g., regression, ANOVA, generalized linear models), there is only one source of random variability. This source of variance is the random sample we take to measure our variables.

It may be patients in a health facility, for whom we take various measures of their medical history to estimate their probability of recovery. Or random variability may come from individual students in a school system, and we use demographic information to predict their grade point averages.

What is the Purpose of a Generalized Linear Mixed Model?

by Kim Love 1 Comment

If you are new to using generalized linear mixed effects models, or if you have heard of them but never used them, you might be wondering about the purpose of a GLMM.

Mixed effects models are useful when we have data with more than one source of random variability. For example, an outcome may be measured more than once on the same person (repeated measures taken over time).

When we do that we have to account for both within-person and across-person variability. A single measure of residual variance can’t account for both.