What is the difference between Clustered, Longitudinal, and Repeated Measures Data? You can use mixed models to analyze all of them. But the issues involved and some of the specifications you choose will differ.
Just recently, I came across a nice discussion about these differences in West, Welch, and Galecki’s (2007) excellent book Linear Mixed Models.
It’s a common question, and there is a lot of overlap in both the study design and in how you will analyze the data from these designs.
West et al give a very nice summary of the three types. Here’s a paraphasing of the differences as they explain them:
In clustered data, the dependent variable is measured once for each subject, but the subjects themselves are somehow grouped (student grouped into classes, for example). There is no ordering to the subjects within the group, so their responses should be equally correlated.
In repeated measures data, the dependent variable is measured more than once for each subject. Usually, there is some independent variable (often called a within-subject factor) that changes with each measurement.
And in longitudinal data, the dependent variable is measured at several time points for each subject, often over a relatively long period of time.
A Few Observations
They also make the following good observations:
1. Dropout is usually not a problem in repeated measures studies, in which all data collection occurs in one sitting. It is a huge issue in longitudinal studies, which usually require multiple contacts with participants for data collection.
2. Longitudinal data can also be clustered. If you follow those students for two years, you have both clustered and longitudinal data. You have to deal with both.
3. It can be hard to distinguish between repeated measures and longitudinal data if the repeated measures occur over time. [My two cents: A pre/post/followup design is a classic example].
4. From an analysis point of view, it doesn’t really matter which one you have. All three are types of hierarchical, nested, or multilevel data. You would analyze them all with some sort of mixed or multilevel analysis. You may of course have extra issues (like dropout) to deal with in some of these.
My Own Observations
I agree with their observations, and I’d like to add a few from my own experience.
1. Repeated measures don’t have to be repeated over time. They can be repeated over space (the right knee gets the control operation and the left knee gets the experimental operation). They can also be repeated over condition (each subject gets both the high and low cognitive load condition. Longitudinal studies are pretty much always over time.
This becomes an issue mainly when you are choosing a covariance structure for the within-subject residuals (as determined by the Repeated statement in SAS’s Proc Mixed or SPSS Mixed). An auto-regressive structure is often needed when some repeated measurements are closer to each other than others (over either time or space). This is not an issue with purely clustered data, since there is no order to the observations within a cluster.
2. Time itself is often an important independent variable in longitudinal studies, but in repeated measures studies, it is usually confounded with some independent variable.
When you’re deciding on an analysis, it’s important to think about the role of time. Time is not important in an experiment, where each measurement is a different condition (with order often randomized). But it’s very important in a study designed to measure changes in a dependent variable over the course of 3 decades.
3. Time may be measured with some proxy like Age or Order. But it’s still really about time.
4. A longitudinal study does not have to be over years. You could be measuring reaction time every second for a minute. In cases like this, dropout isn’t an issue, although time is an important predictor.
5. Consider whether it makes sense to think about time as continuous or categorical. If you have only two time points, even if you have numerical measurements for them, there isn’t a point in treating it as continuous. You need at least three time points to fit a line, but more is always better.
6. Longitudinal datacan be analyzed with many statistical methods, including structural equation modeling and survival analysis. You only use multilevel modeling if the dependent variable is measured repeatedly and if the point of the model is to see how it changes (or differs).
Naming a data structure, design, or analysis is most helpful if it is so specific that it defines yours exactly. Your repeated measures analysis may not be like the repeated measures example you’re trying to follow. Rather than trying to name the analysis or the data structure, think about the issues involved in your design, your hypotheses, and your data. Work with them accordingly.
If you’ve ever run a one-way analysis of variance (ANOVA), you’re familiar with post-hoc tests. The ANOVA omnibus test only tells you whether any groups differ in their means. But if you want to explore which specific group mean is different from which, you need to follow up with a post-hoc test.
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One big advantage of R is its breadth. If anything has been done in statistics, there is an R package that will do it.
The problem is that sometimes there are four packages that will do it. This is big problem with R (and with Python for that matter). (more…)
When you need to compare a numeric outcome for two groups, what analysis do you think of first? Chances are, it’s the independent samples t-test. But that’s not the only, or always, the best option. In many situations, the Mann-Whitney U test is a better option.
The non-parametric Mann-Whitney U test is also called the Mann-Whitney-Wilcoxon test, or the Wilcoxon rank sum test. Non-parametric means that the hypothesis it’s testing is not about the parameter of a particular distribution.
It is part of a subgroup of non-parametric tests that are rank based. That means that the specific values of the outcomes are not important, only their order. In other words, we will be ranking the outcomes.
Like the t-test, this analysis tests whether two independent groups have similar typical outcomes. You can use it with numeric data, but unlike the t-test, it also works with ordinal data. Like the t-test, it is designed for comparisons, and not for estimation or prediction.
The biggest difference from the t-test is that it does not compare means. The Mann-Whitney U test determines whether a random observation from one group tends to be higher (or lower) than a random observation from the other group. Imagine choosing two observations, one from each group, over and over again. This test will determine whether one group is more likely to have the higher values.
It has many advantages: It is a straightforward comparison of means. There are versions for similar and different variances in the two groups. Many people are familiar with it.
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If you have a categorical predictor variable that you plan to use in a regression analysis in SPSS, there are a couple ways to do it.
You can use the SPSS Regression procedure. Or you can use SPSS General Linear Model–>Univariate, which I discuss here. If you use Syntax, it’s the UNIANOVA command.
The big question in SPSS GLM is what goes where. As I’ve detailed in another post, any continuous independent variable goes into covariates. And don’t use random factors at all unless you really know what you’re doing.
So the question is what to do with your categorical variables. You have two choices, and each has advantages and disadvantages.
The easiest is to put categorical variables in Fixed Factors. SPSS GLM will dummy code those variables for you, which is quite convenient if your categorical variable has more than two categories.
However, there are some defaults you need to be aware of that may or may not make this a good choice.
The dummy coding reference group default
SPSS GLM always makes the reference group the one that comes last alphabetically.
So if the values you input are strings, it will be the one that comes last. If those values are numbers, it will be the highest one.
Not all procedures in SPSS use this default so double check the default if you’re using something else. Some procedures in SPSS let you change the default, but GLM doesn’t.
In some studies it really doesn’t matter which is the reference group.
But in others, interpreting regression coefficients will be a whole lot easier if you choose a group that makes a good comparison such as a control group or the most common group in the data.
If you want that to be the reference group in SPSS GLM, make it come last alphabetically. I’ve been known to do things like change my data so that the control group becomes something like ZControl. (But create a new variable–never overwrite original data).
It really can get confusing, though, if the variable was already dummy coded–if it already had values of 0 and 1. Because 1 comes last alphabetically, SPSS GLM will make that group the reference group and internally code it as 0.
This can really lead to confusion when interpreting coefficients. It’s not impossible if you’re paying attention, but you do have to pay attention. It’s generally better to recode the variable so that you don’t confuse yourself. And while you may believe you’re up for overcoming the confusion, why make things harder on yourself or with any other colleague you’re sharing results with?
Interactions among fixed factors default
There is another key default to keep in mind. GLM will automatically create interactions between any and all variables you specify as Fixed Factors.
If you put 5 variables in Fixed Factors, you’ll get a lot of interactions. SPSS will automatically create all 2-way, 3-way, 4-way, and even a 5-way interaction among those 5 variables.
That’s a lot of interactions.
In contrast, GLM doesn’t create by default any interactions between Covariates or between Covariates and Fixed Factors.
So you may find you have more interactions than you wanted among your categorical predictors. And fewer interactions than you wanted among numerical predictors.
There is no reason to use the default. You can override it quite easily.
Just click on the Model button. Then choose “Custom Model.” You can then choose which interactions you do, or don’t, want in the model.
If you’re using SPSS syntax, simply add the interactions you want to the /Design subcommand.
So think about which interactions you want in the model. And take a look at whether your variables are already dummy coded.
Formatting Date Variables seems like it should be straightforward, but sadly, it’s not.
If you are given data that includes dates, expect confusion. Dates can be represented in many different ways. (more…)
