Week 10: Longitudinal II

Models for Longitudinal Data II

Week Learning Objectives

By the end of this module, you will be able to

  • Specify models with alternative error covariance structures
  • Describe the difference between analyzing trends vs. analyzing fluctuations with longitudinal data
  • Run analyses with time-varying predictors (i.e., level-1 predictors)
  • Interpret and plot results

Task List

  1. Review the resources (lecture videos and slides)
  2. Complete the assigned readings
  3. Attend the Tuesday session to learn about brms
  4. Attend the Thursday session and participate in the class exercise
  5. Complete Homework 8
  6. (Optional) Read the bonus R code on the generalized estimating equations (GEE) method

Lecture

Slides

PDF version

In the videos for this week, you will see that I used the R package glmmTMB for frequentist analyses for fitting models with autoregressive covariance structures. These are useful for getting quick results, but they may sometimes run into convergence issues. Using brms is generally more stable.

Check your learning
Assume that the temporal correlation decreases with a longer time gap. A researcher collects data at baseline (Time 1), 3-month follow-up (Time 2), and then 5-month follow-up (Time 3). Which correlation should be strongest?



Covariance Structure in MLM

OLS and RI-MLM/RM-ANOVA

Check your learning
The random-intercept model/repeated-measures ANOVA assumes a specific temporal covariance structure. What is that structure called?




Random Slopes

Autoregressive(1) error structure

Check your learning
In an AR(1) covariance structure, what is the implied correlation between Time 2 and Time 4, if \(\rho = .4\)?

Check your learning
When analyzing a conversation between a couple, a researcher is interested in whether a person follows up the partner’s complaints with positive or negative behaviors. Is this an example of studying trends or fluctuations?

Model 1

Check your learning
In the model discussed in the video, what is the interpretation of the contextual effect of mood1?



Model 2

Note

For the coefficients of stressor and stressor_pm in the above model, the coefficients are ones adjusting for the other predictors in the model (e.g., mood1_pm, mood1_pmc, women, and their interactions).