Week 8

Models for Longitudinal Data I

Week Learning Objectives

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

• Describe the similarities and differences between longitudinal data and cross-sectional clustered data
• Perform some basic attrition analyses
• Specify and run growth curve analysis
• Analyze models with time-invariant covariates (i.e., lv-2 predictors) and interpret the results
• Create a GitHub repository to be used for your class project

Task Lists

1. Review the resources (lecture videos and slides)
2. Complete the assigned readings
   • Snijders & Bosker ch 15 (you can skip 15.1.3 and 15.1.4)
3. Prepare the prospectus and schedule a meeting with the instructor
4. Additional resources for learning MLM for longitudinal data analysis
   • This excellent book by Hoffman (2014) (USC SSO required)
5. HW 8 is not due until October 30, but you may start working on Part A of it

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

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Check your learning: In a research study, data were collected for a group of patients on symptoms of eating disorder on a weekly interval across 5 weeks. What type of data is this?

Panel data
Intensive longitudinal data
Cross-sectional data

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Example data

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Check your learning: In the data set, at what level is homecog, which is a measure of mother’s cognitive stimulation at baseline?

Level 1 Level 2

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Basic attrition analysis

See the R code section.

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Check your learning: In the spaghetti plot, what does the average trend line mean?

That every child showed an increasing trend
That the sample average reading score increased across time
That there is no variability in individual trajectories

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Growth Curve Modeling

Note that in the video, the function brm() from the brms package was used for Bayesian analyses. However, in this class we will use the glmmTMB() function instead (see the updated slides). The parameter estimates and interpretations are basically the same.

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Thinking exercise: In a growth model, what does it mean when \(\tau_1 = 0\)?

That on average, there is no change on the outcome across time
That every participant has the same rate of change
That every participant has the same outcome score

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Linear growth

Note that what is labelled as SD_post is the Bayesian analogue of the standard error.

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Check you learning: What is the advantage of having time to start at 0?

The intercept corresponds to the predicted score at the first time point
So that tau_1 will be the SD of the slopes

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Piecewise linear growth

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Practice yourself: What should the coding of phase 1 and phase 2 be if the turning point is set at time = 2?

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Instead of using the LOOIC in the Bayesian analysis as discussed in the video, we can use the more popular AIC statistic to compare the two models.

Note: In this example, the turning point was chosen mostly based on the spaghetti plot and was arbitrary. For your research, you should justify your choice.

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Check your learning: If a piecewise growth model has an AIC of 23745, and a linear growth model has an AIC of 23650, which model should be preferred?

Piecewise Linear

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Time-Invariant Covariates

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Thinking exercise: What does the coefficient for phase1 mean when the model includes an interaction between phase1 and homecog9?

The average slope from time 0 to time 1
The average slope from time 0 to time 1 for kids with homecog = 9
The average slope from time 0 to time 1, holding constant homecog

Varying Occasions

Instead of using time as the duration since a particular point in history (e.g., when the study started), one can use some other ways of quantifying time, such as the duration since one is born (i.e., chronological age). See R code.

Using GitHub

First, create a GitHub account at github.com. You can see some advice at https://happygitwithr.com/github-acct.html

Check out this page for system-specific instructions for installing Git: https://happygitwithr.com/install-git.html

Check out this page for getting a personal access token (PAT) for GitHub: https://happygitwithr.com/credential-caching.html#get-a-pat

As an example, here is the GitHub repository for this class website: https://github.com/marklhc/20213-psyc575-usc