Week 10

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 Lists

1. Review the resources (lecture videos and slides)
2. Complete the assigned readings
   • Hoffman (2014) ch 4.1 (USC SSO required)
   • Hoffman (2014) ch 8 (USC SSO required)
3. Attend the Thursday session and participate in the class exercise
4. Complete Homework 8
5. (Optional) Read the bonus R code on the generalized estimating equations (GEE) method
   • Additional reference: https://journals.sagepub.com/doi/abs/10.3102/10769986211017480

Lecture

Slides

Note that in some of the videos below the Bayeisan analyses were used; however, for the class this year we will stay with frequentist analyses. The results and interpretations are basically; just note some differences in the terminology.

You can view and download the slides here: PDF

Longitudinal Data Analysis II

Temporal Covariance/Correlation

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?

Between Time 1 and Time 2
Between Time 2 and Time 3
Between Time 1 and Time 3

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?

Independence
Autoregressive
Autoregressive and Moving Average
Compound Symmetry

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 \(\rho = .4\)?

.4 .2 .16 .064

Analyzing Dynamics

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

Trends Fluctuations

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Model 1

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Check your learning: In the model above, what is the interpretation of the contextual effect of mood1?

The predicted difference in average symptoms between two individuals with 1 unit difference in average negative mood
The predicted difference in symptoms for an individual across two days with 1 unit difference in mood
The predicted difference in symptoms between two individuals with 1 unit difference in average negative mood on a day when both individuals have the same daily mood level

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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).