# 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

- Review the resources (lecture videos and slides)
- Complete the assigned readings
- 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

# 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?

## 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