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Ordinal (ordered) logistic regression model. Used to model an ordered response â for example, low, medium, or high. Might also be called the ordinal multinomial logit model. Ordinal logistic models take into account the ordered nature of the response, which can result in simple, more powerful models.
This one is relatively simple. Very similar names for two totally different concepts. Hierarchical Models (aka Hierarchical Linear Models or HLM) are a type of linear regression models in which the observations fall into hierarchical, or completely nested levels. Hierarchical Models are a type of Multilevel Models.