# Treating data points that belong to several categories in regressions

**URL:** <https://discourse.datamethods.org/t/treating-data-points-that-belong-to-several-categories-in-regressions/5053>\
**Category:** models\
**Tags:** model-specification\
**Created:** [November 3, 2021, 7:47am UTC](https://discourse.datamethods.org/t/treating-data-points-that-belong-to-several-categories-in-regressions/5053 "2021-11-03T07:47:01Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Tomer\_Milo](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/tomer_milo/32/2495_2.png) [@Tomer\_Milo](https://discourse.datamethods.org/u/Tomer_Milo)\
**Post date:** [November 3, 2021, 7:47am UTC](https://discourse.datamethods.org/t/treating-data-points-that-belong-to-several-categories-in-regressions/5053/1 "2021-11-03T07:47:01Z")

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Assume a simple linear regression model with varying intercepts and slopes:

![y_i = a_{category_i} + b_{category_i}*x_i](https://discourse.datamethods.org/uploads/default/original/2X/c/cd49d4a8a8332f1f6d97ced59b7d57fecb096ba6.gif)

I have a dataset with one continuous predictor (x) and one categorial predictor (“category”). Let’s say 2 categories. I want to infer a1, a2, b1, b2.

How should I treat data points that belong to both of these categories?

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**Author:** ![f2harrell](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/f2harrell/32/165_2.png) [@f2harrell](https://discourse.datamethods.org/u/f2harrell)\
**Post date:** [November 3, 2021, 12:08pm UTC](https://discourse.datamethods.org/t/treating-data-points-that-belong-to-several-categories-in-regressions/5053/2 "2021-11-03T12:08:23Z")

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I don’t see where you have a main effect for b. Lack of main effects does not respect the hierarchy principle and will make the result very dependent on the coding of x.