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Is it acceptable (publishable) to run a multilevel model with only level-2 and level-3 predictors? Example: Looking only at the effect of school resources, size or location, and at the district level (budget etc.). The dataset does not contain individual level variables (e.g. gender, SES etc.)

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Yes, it's acceptable. Sometimes you don't have level 1 predictors. If you don't have them, you can't use them.

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For whatever reason, the bot bumped this post. While Jeremy is correct, I would also add that while there may not be level-1 predictors or the data for it, in many cases, aggregate data exists at higher levels. E.g., SES at level one might be captured by median income, %male, or %white for a school or for a district and would still be relevant. So while it is not necessary to have level-1 predictors, you should consider adding aggregate predictors. Though they may not be a perfect substitute, they would be the next best option.

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    $\begingroup$ Id forgotten about this answer. Thanks for the clarification. $\endgroup$ Commented Jun 3 at 14:15

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