Multilevel modeling and longitudinal data

There are a couple of broad categories of modeling approaches that are mentioned in this article

1. Random Intercept (RI)
2. Random Slope (RS)
3. Random Intercept and Slope (RIAS)

Random Intercept Model

Do you have groupings in your data such that the impact of the explanatory variable should be the same in each group but the actual value of the outcome variable is different?

A random intercept model may be appropriate. For example, you may be studying different classrooms in the same school but the students have different starting skills in each classroom. Perhaps all the teachers are using the same curriculum, and you therefore expect a similar impact across classrooms.

The assumption of equal slopes may not be appropriate if the impact of the explanatory variable is large in some groups than others. In some cases, a dataset has just enough power for a RI model.

Random Slopes model

For example, you may have a longitudinal dataset in which the starting value of the metric of interest has low variance across the population you are modeling, but the magnitude of the effect of the explanatory variable has high variance where certain groups see a larger effect.

Random Intercept and Slope

This model is useful for many types of data but there involves the highest number of parameters. Your dataset must have sufficient power.