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?
This webinar will present the steps to apply a type of latent class analysis on longitudinal data commonly known as growth mixture model (GMM). This family of models is a natural extension of the latent variable model. GMM combines longitudinal data analysis and Latent Class Analysis to extract the probabilities of each case to belong to latent trajectories with different model parameters. A brief (not exhaustive) list of steps to prepare, analyze and interpret GMM will be presented. A published case will be described to exemplify an application of GMM and its complexity.
Finally, an alternative approach to GMM will be presented where the longitudinal model approach is linear mixed effects (also known as hierarchical linear model or multilevel modeling). The idea is the same as in GMM using growth curve modeling, mainly that the latent class membership specifies specific unobserved trajectories. These models are equivalent to GMM and are sometimes referred to heterogeneous linear mixed effects, underlining the idea that the sample may not belong to one single homogeneous population, but potentially to a mixture of distributions.
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.
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 both in 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.
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, but 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, or multilevel data, and 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.
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). 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 changes in reaction time every second for a minute. In cases like this, dropout again 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 studies can 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 usually 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 if some of these issues differ. Rather than trying to name the analysis or the data structure, think about the issues involved in your design, your hypotheses, and your data, and work with them accordingly.