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Can I interpret my my coefficient's p-values even I violated the error normality assumptions? I have a large sample size.

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    $\begingroup$ You have linked to tags of ridge regression and glmmlasso. If your regression involves such penalized methods, then standard p-value calculations don't apply in any event. Please say a bit more (by editing your question) about the particular situation you are facing, as the answer may differ between penalized and ordinary regressions. $\endgroup$
    – EdM
    Jul 29, 2018 at 18:49
  • $\begingroup$ You've got to edit the phrasing of your question. We have a lot of international readers who won't understand what's being asked $\endgroup$
    – Aksakal
    Jul 30, 2018 at 13:46

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I'm assuming you're fitting a linear model.

If your residuals are not normally distributed then your model is misspecified so you shouldn't test hypotheses based on this model. You should change your model and use some selection procedures to select the best one using a range of different indicators (AIC, R^2 etc), including plotting the residuals.

If you want more help I suggest including more detail in your question.

EDIT: I got confused, I apologise. If you're seeing a pattern in the residuals (i.e. for plots of residuals vs predictors or residuals vs response) then your model is probably misspecified. The residuals not being normal still means you can't do hypothesis tests on the coefficients though.

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  • $\begingroup$ What should I do to know if the interaction term is significant in my model. Can I cross validate two models and compare their MSEs? one with no interaction and the other model has the interaction. Is it a valid approach? $\endgroup$ Jul 29, 2018 at 18:11
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    $\begingroup$ If your sample size is really large, non normality of residuals does not matter much. $\endgroup$ Jul 29, 2018 at 18:57
  • $\begingroup$ so can I just test hypothesized based on the model? $\endgroup$ Jul 29, 2018 at 19:10
  • $\begingroup$ AIC (or anything else involving the response) based selection introduces bias in inference rather than reduce it. $\endgroup$
    – Michael M
    Jul 29, 2018 at 19:52
  • $\begingroup$ How so @MichaelM? $\endgroup$ Jul 30, 2018 at 6:04

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