Week 8: Cross-Classified Models

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 List

  1. Review the resources (lecture videos and slides)
  2. Complete the assigned readings
  3. Attend the Tuesday session and participate in the class exercise
  4. Complete the project prospectus
  5. Complete Homework 7 (due in two weeks)
  6. Additional resources for learning MLM for experimental designs

Lecture

Slides

PDF version

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?



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



Check your learning

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


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

When there is > 1 observations per cell, one can (and should) estimate the interaction variance component using

lg_rt ~ (1 | id) + (1 | Item) + (1 | id:Item)
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

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




Full Model

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