Week 7

Multilevel Models for Experimental Data

Week Learning Objectives

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

• Identify the correct levels with experimental studies
• Describe designs with crossed random levels
• Assign variables to appropriate levels, and tell which variables can have random slopes at which levels
• Compute a version of effect size (\(R^2\)) for experimental data

Note: In the video the slides use \(d\) for effect size, but we will use \(R^2\) in this class.

Task Lists

1. Review the resources (lecture videos and slides)
2. Complete the assigned readings
   • Snijders & Bosker 13.1
   • Hoffman & Rovine (2007)
3. Attend the Thursday session and participate in the class exercise
4. Complete Homework 7
5. Think about your project—Prospectus will be due in two weeks
6. Additional resources for learning MLM for experimental designs
   • This paper by Judd et al. 

Lecture

Slides

You can view and download the slides here: PDF

Multilevel Experiments

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Check your learning: In a research study, 10 hospitals are randomly assigned to a treatment condition to adopt a new drug, whereas the other 10 hospitals use the conventional method. What is the design of this study?

A cluster-randomized trial
A multisite trial
A within-subjects design

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Example

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Check your learning: In the data set, how many observations are there at level 1?

7,803 153 51

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Long vs. Wide data set

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Check your learning: In the following data, hvltt to hvltt4 are the test score of a verbal learning test across four time points. Is this a long or a wide data set?

long wide

Crossed Random Levels

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Think more: What is the data structure if there are 1,000 students from 100 schools and 30 neighborhoods, and each school has students from multiple neighborhoods?

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Unconditional model

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Practice yourself: Compute the design effects for the person level and for the item level. Do the design effects suggest the need for both levels? (That is, are both design effects > 1.1?)

Answer: See the computation in the R code

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Cross-Classified Random-Effect Model With Random Slopes

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Check your learning: If in the experiment, each person respond to each item 3 times, each time with a different duration. At what level(s) can duration have random slopes?

Both person and item
Person only
Item only
Within-cell

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Full Model

Effect Size

Please check out the slides and the examples in the R code