# Five Advantages of Running Repeated Measures ANOVA as a Mixed Model

Karen Grace-Martin (founder of The Analysis Factor) runs webinars and courses. She uses SPSS and R and has articles on her site to which you can post comments.

There are two ways to run a repeated measures analysis.The traditional way is to treat it as a multivariate test–each response is considered a separate variable.The other way is to it as a mixed model.While the multivariate approach is easy to run and quite intuitive, there are a number of advantages to running a repeated measures analysis as a mixed model.

First I will explain the difference between the approaches, then briefly describe some of the advantages of using the mixed models approach.

Let’s use as an example a data set of students, who are measured at four time points across a school year.The children are given reading tests at the beginning of first grade and at three other time points evenly spaced across the school year. So each child has four observations for reading tests. Let’s assume the children are assigned to different experimental groups, and other covariates are measured.

In the multivariate approach, each child would have a single row of data in the data spreadsheet and four columns for the four reading scores. This is called the wide data form and the unit of observation is considered a child.Covariates that do not change across time, such as sex or age at time 1, would each appear in a column.

In the mixed model approach, each child would have four rows of data.One column would contain the time of measurement and another the reading score. This is called the long format, and the unit of observation is considered one time point per child.Covariates that don’t change would have repeated values across the four rows of data. A time-varying covariate would change values across the four rows, but only one column is needed for each one.

Some advantages of using a Mixed Models Approach: 1.Missing Data: The default approach to missing data in nearly all statistical packages is Listwise Deletion, which drops any observation with any missing data on any variable involved in the analysis. If the percentage missing is small and the missing data are a random sample of the data set, this is a reasonable approach.In the multivariate approach, if a child is missing one time point, they will be dropped from the entire analysis.In the mixed approach, only that time point will be dropped. The remaining data will be retained. 2.Post hoc tests: Because of the way the Sums of Squares are calculated in the multivariate approach, post-hoc tests are not available for repeated measures factors. They are available, however, using the mixed approach. 3.Flexibility in treating time as continuous: Depending on the design of the study, rather than consider time as four categories, it can be more accurate to treat time as a continuous variable. This allows you to model a regression line for time, rather than estimate four means.(You need at least 3 time points to do this, but more are better).This is not possible in the multivariate approach, but simple in the mixed approach. 4.A single dependent variable can be used in other analyses: For example, in a study I’m currently working on, a two-factor (2×4) repeated measures design was used to study whether the impact of these two factors on an outcome was mediated by a third variable. Each subject has eight values of the mediator (one for each of the conditions) and eight values on the final outcome. The mediator is both an outcome and a predictor variable in two different models in this path analysis. Therefore, it was necessary to have a single outcome variable, not eight, in order to have a single path coefficient between the mediator and the outcome. 5.Easier to build into larger mixed models: If our school design happened to also cluster children within teachers, we would need to include teacher as another level in the mixed model. Changing a two to a three level model is simple to do (in practice, if not conceptually) if the model is already set up as a mixed model.

And a bonus reason may be the most important one of all. You, the data analyst, becomes familiar with the terminology, concepts, and programming involved with mixed models in a simple repeated measures design. Then, when you encounter something more complicated (which you most likely will), your learning curve will be a single step, not a giant leap.