Mixed and Multilevel Models

Member Training: Elements of Experimental Design

August 1st, 2019 by

Whether or not you run experiments, there are elements of experimental design that affect how you need to analyze many types of studies.

The most fundamental of these are replication, randomization, and blocking. These key design elements come up in studies under all sorts of names: trials, replicates, multi-level nesting, repeated measures. Any data set that requires mixed or multilevel models has some of these design elements. (more…)

Regression Diagnostics in Generalized Linear Mixed Models

March 25th, 2019 by

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

February 25th, 2019 by

Stage 2Multicollinearity 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

January 9th, 2019 by

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. (more…)

Member Training: Latent Growth Curve Models

October 1st, 2018 by
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?

Understanding Random Effects in Mixed Models

September 17th, 2018 by

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.