Quartz | Level 8

## proc mixed assumption

Hello all,

Any help will be appreciated to help me find a solution for my problem.

My question is that if we apply proc mixed to find model for multilevel repeated measures while the response variable does not have normal distribution, will the estimates be biased? if yes how can i solve the issue? How can i find out what distribution my response has other than histogram? If my response has exponential or other distribution, how can i find the right distribution?

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Accepted Solutions
Diamond | Level 26

## Re: proc mixed assumption

There is no such assumption that the response variable has to be normally distributed.

In this type of modeling, the errors have to be independent and identically distributed according to some normal distribution.

https://blogs.sas.com/content/iml/2018/08/27/on-the-assumptions-and-misconceptions-of-linear-regress...

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Paige Miller
9 REPLIES 9
Diamond | Level 26

## Re: proc mixed assumption

There is no such assumption that the response variable has to be normally distributed.

In this type of modeling, the errors have to be independent and identically distributed according to some normal distribution.

https://blogs.sas.com/content/iml/2018/08/27/on-the-assumptions-and-misconceptions-of-linear-regress...

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Paige Miller
Quartz | Level 8

## Re: proc mixed assumption

Thanks for your reply. But because the observations are repeated measures so they are correlated, should the errors be dependent?
Diamond | Level 26

## Re: proc mixed assumption

I think properly specified repeated measures models handle this type of potential dependency between the repeated measures.

Again, it's the errors that have to be independent and normally distributed, not the values of the response variable.

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Paige Miller
Super User

## Re: proc mixed assumption

Yes. I think so. It is about R-side random effect .
Super User

## Re: proc mixed assumption

You could check Goodness-of-test , like AIC BIC ....... which is smaller and better to fit data.
@Rick_SAS know more something .

@lvm @StatDave @SteveDenham

## Re: proc mixed assumption

The information criteria have to be used carefully.  In order to be effective in selecting a model (or a distribution), the data must be identical in the two instances.  This rules out comparing something with an identity link (like lognormal) to something with a log link (like exponential), or normal (identity) vs almost any other distribution modeled by GLIMMIX.

A good introduction to the assumptions in mixed modeling can be found in SAS for Mixed Models (Stroup et al.) or Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS by Ed Vonesh.  The latter may be quite useful to you, given your short description of your data.

SteveDenham

SAS Super FREQ

## Re: proc mixed assumption

Independent errors is never one of the model assumptions for mixed models. Normal distribution with the variance covariance matrix of R is one of the model assumptions. You would use the REPEATED statement in PROC MIXED to model the correlated residuals. Or, you could use the RANDOM statement to model the the correlated observations in the response.

If you do a residual analysis in PROC MIXED, how non-normal does it look like? One way is to use PROC GLIMMIX to model your data if a different distribution (from the exponential family) is more appropriate.

Diamond | Level 26

## Re: proc mixed assumption

@jiltao wrote:

Independent errors is never one of the model assumptions for mixed models. Normal distribution with the variance covariance matrix of R is one of the model assumptions.

Thanks for the correction!

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Paige Miller
Quartz | Level 8

## Re: proc mixed assumption

Thanks a lot for your valuable responses,

My data is multilevel longitudinal repeated measures over time which is not growth data (is not longitudinal growth data) as i understood response variable does not need to be normally distributed, so if i apply glimmix and my response does not look normal how can i find what distribution should i select in dist section of model statement in proc glimmix?

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