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Supposed I have a mixed model in the form: $$y = X\beta + Zu+ \varepsilon$$

If I want to enforce a constraint on the $\beta$s can I follow the data augmentation approach that @whuber mentioned here: How to apply a soft coefficient constraint to an OLS regression?? What is the best way to enforce coefficient constraints through data augmentation for a linear mixed model?

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No @whuber was not really recommending this approach. I would say the standard software approach, at least in R, is using offset.

Ie if you want to regularise around b instead of 0, then add an offset of Xb, then your coefficients are for (Beta-b)

See offset Param in

https://www.rdocumentation.org/packages/lme4/versions/1.1-21/topics/lmer

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  • $\begingroup$ What do you mean by "le" Also, I am using SAS currently. Why wouldn't the data augmentation approach be recommended? $\endgroup$ – lord12 Mar 23 '20 at 7:36
  • $\begingroup$ from whubers response:"Although you can obtain the solution 𝑏̂ this way, I doubt any of the statistics coming out of this fit will be meaningful." $\endgroup$ – seanv507 Mar 23 '20 at 9:17

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