Mixed and Multilevel Models

Member Training: Hierarchical Regressions

Hierarchical regression is a very common approach to model building that allows you to see the incremental contribution to a model of sets of predictor variables.

Popular for linear regression in many fields, the approach can be used in any type of regression model — logistic regression, linear mixed models, or even ANOVA.

In this webinar, we’ll go over the concepts and steps, and we’ll look at how it can be useful in different contexts.

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.

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About the Instructor

Karen Grace-Martin helps statistics practitioners gain an intuitive understanding of how statistics is applied to real data in research studies.

She has guided and trained researchers through their statistical analysis for over 15 years as a statistical consultant at Cornell University and through The Analysis Factor. She has master’s degrees in both applied statistics and social psychology and is an expert in SPSS and SAS.

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

by Karen Grace-Martin 4 Comments

Have you ever been told you need to run a mixed (aka: 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. [Read more…] about Concepts you Need to Understand to Run a Mixed or Multilevel Model

Analyzing Pre-Post Data with Repeated Measures or ANCOVA

by Karen Grace-Martin 87 Comments

One area in statistics where I see conflicting advice is how to analyze pre-post data. I’ve seen this myself in consulting. A few years ago, I received a call from a distressed client. Let’s call her Nancy.

Nancy had asked for advice about how to run a repeated measures analysis. The advisor told Nancy that actually, a repeated measures analysis was inappropriate for her data.

Nancy was sure repeated measures was appropriate. This advice led her to fear that she had grossly misunderstood a very basic tenet in her statistical training.

The Study Design

Nancy had measured a response variable at two time points for two groups. The intervention group received a treatment and a control group did not. Participants were randomly assigned to one of the two groups.

The researcher measured each participant before and after the intervention.

Analyzing the Pre-Post Data

Nancy was sure that this was a classic repeated measures experiment. It has [Read more…] about Analyzing Pre-Post Data with Repeated Measures or ANCOVA

Three Issues in Sample Size Estimates for Multilevel Models

by Karen Grace-Martin 4 Comments

If you’ve ever worked with multilevel models, you know that they are an extension of linear models. For a researcher learning them, this is both good and bad news.

The good side is that many of the concepts, calculations, and results are familiar. The down side of the extension is that everything is more complicated in multilevel models.

This includes power and sample size calculations. [Read more…] about Three Issues in Sample Size Estimates for Multilevel Models

The Unstructured Covariance Matrix: When It Does and Doesn’t Work

by Karen Grace-Martin 3 Comments

If you’ve ever done any sort of repeated measures analysis or mixed models, you’ve probably heard of the unstructured covariance matrix. They can be extremely useful, but they can also blow up a model if not used appropriately. In this article I will investigate some situations when they work well and some when they don’t work at all.

The Unstructured Covariance Matrix

The easiest to understand, but most complex to estimate, type of covariance matrix is called an unstructured matrix. Unstructured means you’re not imposing any constraints on the values. For example, if we had a good theoretical justification that all variances were equal, we could impose that constraint and have to only estimate one variance value for every variance in the table.

But in an unstructured covariance matrix there are no constraints. Each [Read more…] about The Unstructured Covariance Matrix: When It Does and Doesn’t Work

Sample Size Estimates for Multilevel Randomized Trials

by Karen Grace-Martin 2 Comments

If you learned much about calculating power or sample sizes in your statistics classes, chances are, it was on something very, very simple, like a z-test.

But there are many design issues that affect power in a study that go way beyond a z-test. Like:

repeated measures
clustering of individuals
blocking
including covariates in a model

Regular sample size software can accommodate some of these issues, but not all. And there is just something wonderful about finding a tool that does just what you need it to.

Especially when it’s free.

Enter Optimal Design Plus Empirical Evidence software. [Read more…] about Sample Size Estimates for Multilevel Randomized Trials