Concepts you Need to Understand to Run a Mixed or Multilevel Model

January 23, 2013

(This article was originally published at The Analysis Factor, and syndicated at StatsBlogs.)

Have you ever been told you need to run a multilevel model and been thrown off by all the new vocabulary?

It happened to me when I first started my statistical consulting job, oh so many years ago. I had learned mixed models in an ANOVA class, so I had a pretty good grasp on many of the concepts.

But when I started my job, SAS had just recently come out with Proc Mixed, and it was the first time I had to actually implement a true multilevel model.  I was out of school, so I had to figure it out on the job.

And even with my background, I had a pretty steep learning curve to get to a point where it made sense.  Sure, I was able to figure out the steps, but there are some pretty tricky situations and complicated designs out there.

To implement it well, you need a good understanding of the big picture, and how the small parts fit into it.  That’s what took me a while.

Luckily in my job, I was able to see many, many different designs, and that helped me figure out which issues mattered in which contexts.  (I also had two really great mentors).

I realize you, as a researcher, don’t have that vantage point, which is why I develop workshops–to give you the big picture intuitive understanding, and to show you how the big picture relates to specific steps and decisions you need to make in specific situations.

To get started, it really helps to at least understand certain statistical concepts, some of which are specific to mixed models and some which are more general.

Some concepts related to regression and ANOVA:

You may recognize some of these as the topics of some of my newsletter articles, workshops, and free webinars.  I focus on these because they’re the topics I see researchers struggle with as they try to learn harder models, including mixed models.

These are topics that you really want to understand before you ever attempt a mixed model.  Because they’re so universal, I assume participants in my repeated measures workshop already understand them (though we review quite a few of them).

By the way, not all of them currently have links, so I’ll fill these in as I write more articles.

 Interpreting intercepts and regression coefficients


Dummy Coding

How ANOVA and regression are the same model

 Assessing model fit

The measurement of effects of categorical and continuous variables


Correlation and Covariance

Model building

Crossed and Nested Factors

Some concepts that are inherent to mixed models:

The following are the concepts that aren’t relevant to all regression models, but are extremely important in mixed models. You may have come across some of them in other areas of statistics as well–they’re not all unique to mixed models.

These are the topics we go over in great detail in the Repeated Measures workshop, particularly how they related to repeated measures and longitudinal designs.  I’ve linked to some free resources we have on these topics to get you started.

Intra Class Correlation

Maximum Likelihood Estimation, Deviance and -2 Log Likelihood

Fixed and Random Factors

Covariance Structures, as well as the meaning of specific structures, including Compound Symmetry,  Autoregressive, Toeplitz, Unstructured, and others

Information Criteria, like AIC, BIC, AICC

Marginal and Mixed Models

Random Intercepts and Slopes

G and R matrices

Missing at Random




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