Testing normality assumption in linear mixed effects model - How do you do it?

[Fabian.Lenhard]

Hello!

I would greatly appreciate your input on the following problem:
Linear mixed effects model (xtmixed) relies on the assumption that the residuals are normally distributed. How can you test this assumption in stata? Is there for example a way of plotting the residuals against a normalcurve, alternatively a statistical test that does the job?

Suggestions very welcome!

Best

Fabian

[Alfonso Sánchez-Peñalver]

A simple google search produces the following result

https://kb.iu.edu/data/alug.html

[Fabian.Lenhard]

Thank you Alfonso! But how would I for example use Shapiro wilks or a qq plot for the residuals of the mixed effects model?

[Alex Gamma]

Gelman & Hill (2007) note that the normality or otherwise of residuals doesn't affect the parameter estimates in multilevel models. They therefore advise against normality tests of regression residuals (p. 46)

Gelman, A., Hill, J., 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Cambridge.

[Jeff Wooldridge]

I agree with Alex. Testing normality in mixed models is like testing normality for standard random or fixed effects estimation. It is not necessary. MLE is really quasi-MLE and is essentially feasible GLS. Ask yourself this: what would you do if normality is rejected? The answer is the same as it is for linear regression: nothing.

[Bruce Weaver]

In addition to what others have said, normality of the errors is at best an approximation. George Box said it well:

"In applying mathematics to subjects such as physics or statistics we make tentative assumptions about the real world which we know are false but which we believe may be useful nonetheless. The physicist knows that particles have mass and yet certain results, approximating what really happens, may be derived from the assumption that they do not. Equally, the statistician knows, for example, that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world."

Box GEP. Science and Statistics. JASA, Vol. 71, No. 356 (Dec., 1976), 791-799.