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 () for experimental data

Note: In the video the slides use for effect size, but we will use in this class.

Task Lists

Review the resources (lecture videos and slides)
Complete the assigned readings
- Snijders & Bosker 13.1
- Hoffman & Rovine (2007)
Attend the Thursday session and participate in the class exercise
Complete Homework 7
Think about your project—Prospectus will be due in two weeks
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

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?

Example

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

Long vs. Wide data set

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?

ABCDEFGHIJ0123456789

id <int>	hvltt <int>	hvltt2 <int>	hvltt3 <int>	hvltt4 <int>
1	28	28	17	22
2	24	22	20	27
3	24	24	28	27
4	35	34	32	34
5	35	29	34	34
6	29	27	26	29
7	18	16	27	30
8	25	26	25	29
9	24	17	20	11
10	22	19	21	26

Crossed Random Levels

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?

Unconditional model

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

Cross-Classified Random-Effect Model With Random Slopes

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?

Full Model

Effect Size

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