Effect Decomposition, Random Coefficient Model, and Cross-level Interactions

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

- Explain what the ecological fallacy is
- Use
**cluster-mean/group-mean centering**to decompose the effect of a lv-1 predictor - Define
**contextual effects** - Explain the concept of
**random slopes** - Analyze and interpret
**cross-level interaction**effects

- Review the resources (lecture videos and slides)
- Complete the assigned readings
- Snijders & Bosker ch 4.6, 5.1–5.3

- Attend the Thursday session and participate in the class exercise
- Complete Homework 4
- Now that you have learned the basics of MLM, start thinking about your project (Prospectus due around Oct 18)

You can view and download the slides here: PDF

Check your learning: The Type I error inflation problem when using OLS regression for clustered data applies to

Check your learning: In a “bizarre” research finding that found a correlation between chocolate consumption and number of Nobel prize winners at the country level, which of the following is reasonable to infer?

Check your learning: Summarize the “Big-Fish-Little-Pond Effect” in terms of how a person’s own academic performance and the overall performance of the person’s school on academic self-concept.

Note: What I called “cluster-mean centering” is the same as “within-group centering” in Snijders & Bosker (2012)

Check your learning: Why do we need to separate a level-1 predictor into two variables in the model?

Thinking exercise: Based on the between-cluster level component in
the path diagram and in the equations, `meanses`

can
predict

Check your learning: Based on the results shown in the video, is the school-level slope or the student-level slope larger for the association between SES and math achievement?

Try it yourself: Obtain the predicted `mathach`

for
Student B, and compare with Students A and C.

Check your learning: The contextual effect is

Check your learning: In a random-coefficient model, if there are \(J\) cluster, there are

Check your learning: Which combination of \(\tau_0\) and \(\tau_1\) best describes the graph below?

Check your learning: In a random-slope model, if \(\gamma_{10}\) (the average slope) = 0.2, \(\tau^2_1 = 0.04\), what is the 68% plausible range for the slopes across clusters?

In the video, there was a mistake in the path diagram, in that one of the circle should be \(\beta_{1j}\), not \(\beta_{0j}\)

Check your learning: Conceptually, a cross-level interaction is the same as