A recent discussion on the StataList (here) delves into subtle differences that distinguish inserting fixed effects into an ordered logit estimation (ologit) and estimating a model using the feologit command.
As the discussion emphasizes, the appropriate approach pivots largely on different types of "fixed effects." Specifically, the feologit command is more appropriate for longitudinal data. In contrast, inserting fixed effects into an ologit model makes sense where the "fixed effect" refers to time-invariant observation-level "effects."
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