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On the Wikipedia page for Multilevel model it is written that

[M]ultilevel models can be used as an alternative to ANCOVA, where scores on the dependent variable are adjusted for covariates (e.g. individual differences) before testing treatment differences. Multilevel models are able to analyze these experiments without the assumptions of homogeneity-of-regression slopes that is required by ANCOVA.

There is a similar question here in which a user asks how to use Multilevel Modelling to overcome the homogeneity of regression slopes problem in ANCOVA, but is told that they should instead simply add an interaction term to their (formerly) ANCOVA model. The general message from the comments is that using multilevel modelling would be "overkill" here.

My question is different - under what circumstances is it better to resolve the homogeneity of regression slopes issue through multilevel modelling, and under what circumstances is it better to resolve the issue through just adding an interaction term? More generally, I'm wondering how multilevel modelling resolves the heterogeneity of regression slopes issue at all.

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