Hi, I'm new here so let me know if this should go into any particular category.
I would like to ask whether fixed effects models can be used for time-invariant, multilevel data instead of panel data (as an alternative to multilevel modelling)? In this case dummy variables would be included for all level 2 units.
My understanding is that the term, 'fixed effects', relates specifically to the units of observation and the panel data structure, but I don't see why this would be an issue for the model mathematically.
Fixed effects models can be used for time-invariant predictors in your data. These models control for all time-invariant characteristics of individuals (or whatever units are being analyzed), thereby eliminating the possibility that omitted time-invariant characteristics could bias the results. This makes them suitable for scenarios where these characteristics do not change over time, or their impact is constant.
Fixed effects models can also focus on within-unit (e.g., individual, company, country) variations over time. They essentially compare each unit to itself over time, thus controlling for all potential time-invariant confounding variables.