Our plan for today

• Recall the basics of binary logistic models
• Discuss 2 examples of ML binary logistic models
• An exercise (on your own)

Binary multilevel model

• no more complicated than one-level binary response model
• no more complicated than multilevel linear model

A brief recap on binary models

• used when you need to model a binary outcome: 0-1, no-yes, A or B, etc.
• the basic idea is to turn the existing distribution into smth similar to standard normal distribution
• instead of real values you work with cumulative density functions

Probability Density Function vs. Cumulative

Logit as a link

https://www.youtube.com/watch?v=ARfXDSkQf1Y

Interpretation

You obtain regression coefficients like in usual linear model
However, they indicate the changes in log of odds ratio
So, as usually, if your b-coef is positive the log is increasing and visa versa
But, to come to odds ratio you need to calculate exp(b-coef)

Typical multilevel interpretation

random intercept part https://www.rips-irsp.com/articles/10.5334/irsp.90/

Typical multilevel interpretation

random slope part https://www.rips-irsp.com/articles/10.5334/irsp.90/

A brand new ICC for binary model

\[ICC = \frac{\sigma^2 u{0}}{\sigma^2u_{0} + \pi^2 / 3}\] \(\pi^2 / 3 ≈ 3.29\) refers to the standard logistic distribution

Sequence of multilevel analysis