Model Diagnostics and Results Reporting

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

- Describe the major
**assumptions**in basic multilevel models - Conduct analyses to decide whether
**cluster means**and**random slopes**should be included - Use graphical tools to diagnose assumptions of
**linearity**,**homoscedasticity**(equal variance), and**normality** - Solve some basic
**convergence issues** **Report**results of a multilevel analysis based on established guidelines

- Review the resources (lecture videos and slides)
- Complete the assigned readings
- Snijders & Bosker ch 10
- Meteyard & Davies (2020; to be shared on Slack)
- McCoach (2019 chapter) (USC SSO required)

- Attend the Thursday session and participate in the class exercise
- Complete Homework 6

You can view and download the slides here: HTML PDF

Check your learning: Homoscedasticity means

Note: \(\mathrm{E}(Y)\) can also be written as \(\hat Y\), the predicted value of \(Y\) based on the predictor values.

The linear model is also flexible as it can allow predictors that are curvillinear terms, such as \(Y = b_0 + b_1 X_1 + b_2 X_1^2\), or \(Y = b_0 + b_1 \log(X_1)\), or more generally \[Y = b_0 + \sum_{i}^p b_i f(x_1, x_2, \ldots)\] The “linear” part in a linear model actually means that \(Y\) is a linear function of the coefficients \(b_1, b_2, \ldots\).

The second functional form in the slide, however, is a truly nonlinear function.

Check your learning: Which of the following is **NOT** a
linear model?

Check your learning: What is implied when the model specifies that the variance of \(u_{0j}\) is \(\tau^2_0\)?

Check your learning: What does “I” stand for?

Check your learning: What is shown in a marginal model plot?

Check your learning: Which assumption(s) are likely violated in the following plot?

- Outliers/influential observations
- Check coding error
- Don’t drop outliers unless you adjust the standard errors accordingly, or use robust models

- Reliability (e.g., \(\alpha\)
coefficient)
- Reliability may be high at one level but low at another level
- See Lai (2021, doi: 10.1037/met0000287) for level-specific
reliability
- You can use the
`multilevel_alpha()`

function from https://github.com/marklhc/mcfa_reliability_supp/blob/master/multilevel_alpha.R

- You can use the