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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5You 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. – EdM Jul 29 '18 at 18:49
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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 – Aksakal Jul 30 '18 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.
Robert Arbon
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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? – Nikko Joe Ramal Jul 29 '18 at 18:11
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2If your sample size is really large, non normality of residuals does not matter much. – Heteroskedastic Jim Jul 29 '18 at 18:57
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AIC (or anything else involving the response) based selection *introduces* bias in inference rather than *reduce* it. – Michael M Jul 29 '18 at 19:52
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@RobertArbon: the resulting models tend to be overly optimistic, see e.g. the book "Regression Modelling Strategies" of F. Harrell. – Michael M Jul 30 '18 at 06:41