Calcite | Level 5

## Estimates for fixed effects in linear mixed models (Proc Mixed)

Hello,

First time posting here , please forgive errors. My question is about linear mixed models with the standard specification:

y=XB + Zu + e

using Proc Mixed.

See for instance the Wikipedia: https://en.wikipedia.org/wiki/Mixed_model

Could someone please explain why SAS Proc Mixed does not output the B coefficients and their standard errors, like in a standard regression output of Proc Reg, for instance? The B parameter is a meaningful statistical quantity (identifiable parameter in the underlying statistical model), and testing it makes sense in many problems. I believe a maximum likelihood estimator should exist if you assume normal errors and normal distribution for the random effects. Please correct me if necessary.

So why are doesn't SAS return corresponding estimates and standard errors for the components of B and let you do a Wald test, say by default? Is there a way to get them?

Why does it only offer Type III ANOVA analyses? Are the "Estimate" and "Contrast" tests all you can get?

John

7 REPLIES 7
Super User

## Re: Estimates for fixed effects in linear mixed models (Proc Mixed)

Yes. I also confused before. Maybe SAS want save some source to print it all (no need to display).

But you could specify option SOLUTION to get fixed/random effect parameter .

``````proc mixed data=sashelp.class;
class sex;
model height=weight age sex/solution;
run;``````

Why does it only offer Type III ANOVA analyses? Are the "Estimate" and "Contrast" tests all you can get?

Yes. Type3 is just conventient to declare the X variable is significant or not, you can see in Type3 there are only ONE sex to check if it is significant or not, but in Solution in Fixec Effects have TWO sex which is hard to identity sex is significant or not .

If you want more ESTIMATE for a linear combination, check ESTIMATE CONTRAST LSMEANS LSMESTIMATE statement.

BTW, you'd better to post your question at Statistical Forum ,since it is about SAS/STAT:

https://communities.sas.com/t5/Statistical-Procedures/bd-p/statistical_procedures

@StatDave  @SteveDenham  statistical master could give you better explanation and solution.

Calcite | Level 5

## Re: Estimates for fixed effects in linear mixed models (Proc Mixed)

Thank you so much for your help.

John

## Re: Estimates for fixed effects in linear mixed models (Proc Mixed)

I see that you mentioned PROC REG, and are wondering why PROC MIXED doesn't produce the parameters you are used to. Well, it does. In the fixed effect solution table, the Estimate column gives almost what you are expecting. for continuous variables, the estimate is just like what you see from PROC REG. However, the use of categorical variables through the CLASS statement leads to a '0' estimate in the Solution table, which is pretty confusing at first. The reason is that the parameterization in PROC MIXED is non-full rank, i.e. one level of a class variable is set to zero. The other levels of that variable are presented as the difference from the level set to zero, called a reference level in some cases. The documentation for SAS/STAT has some great introductory material that goes through this, so look at Introduction to -- Statistical Modeling with SAS/STAT Software; Regression Procedures; Analysis of Variance Procedures; and Mixed Modeling Procedures, and The Four Types of Estimable Functions. I think all of your questions have answers there.

SteveDenham

Calcite | Level 5

## Estimates for fixed effects in linear mixed models (Proc Mixed)

Hello,

This is my first time asking on this site, I was advised to repost in the statistical forum.  My question is about linear mixed models with the standard specification:

y=XB + Zu + e

using Proc Mixed.

See for instance the Wikipedia: https://en.wikipedia.org/wiki/Mixed_model

Could someone please explain why SAS Proc Mixed does not output the B coefficients and their standard errors, like in a standard regression output of Proc Reg, for instance? The B parameter is a meaningful statistical quantity (identifiable parameter in the underlying statistical model), and testing it makes sense in many problems. I believe a maximum likelihood estimator should exist if you assume normal errors and normal distribution for the random effects. Please correct me if necessary.

So why are doesn't SAS return corresponding estimates and standard errors for the components of B and let you do a Wald test, say by default? Is there a way to get them?

Why does it only offer Type III ANOVA analyses? Are the "Estimate" and "Contrast" tests all you can get?

I'm sure other people have wondered about this too. Any further explanation would help a lot. If I'm missing something conceptually please do straighten me out. Thanks for your help.

John

Super User

## Re: Estimates for fixed effects in linear mixed models (Proc Mixed)

No need to repost. Just call out to one of the Super Users, we'll move your topic for you.

Calcite | Level 5

## Re: Estimates for fixed effects in linear mixed models (Proc Mixed)

Thanks, you appear to be a super user. Would you kindly transfer it for me?

John

Super User