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[Mixed Model 1.5.1] Introduction to the Theory of General Linear Mixed Models 2018.01.19
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[Mixed Model 1.5.1] Introduction to the Theory of General Linear Mixed Models

 


ȳϼ^^

 


̹ ðʹ General linear mixed model ˾ƺٵ,

, Ϲ ˰ ִ general linear models general linear mixed model 񱳿 ⺻ ̷п ˾ƺ ϰڽϴ.

 


General linear models General linear mixed model ⺻ ̷

Toy

ML REML

ȿ GLS

 

 


GLM vs GLMM

GLM Procedure Model

 

 



Ϳ

𵨿 ˷(known) matrix

˷ (unknown) fixed effect

Random errors



0 л Ժ ̶ մϴ.


׷Ƿ general linear model ,

 and  ̸,      Դϴ.

 


,  and  ̸,  Դϴ.


 


 


MIXED Procedure Model

 



Ϳ

Fixed effect ˷(known) matrix

PROC MIXED MODEL Ǵ

˷ (unknown) fixed effect

Random effect ˷(known) matrix

PROC MIXED RANDOM Ǵ

˷ (unknown) random effect

Random errors


 


    ̰, Ʒ հ л Ժ .

 

 

 

 


PROC MIXED ϸ G, RĿ پ л ֽϴ.


ռ Ͽ Toy ,   ̰ л default Ǵ ⺻ Ǿϴ.


, y ؼ  and  Դϴ.



 

 

MIXED Procedure Model

 

 

PROC MIXED MODEL Ͽ fixed effects ϰ

RANDOM Ͽ Ư random effects,

REPEATED Ͽ Ư л-л errors ֽϴ.

 

PROC MIXED RANDOM REPEATED

쿡 Ư л-л ı Բ statements( , REPEATED statement) л Ͽ, ٸ statements( , RANDOM statement) ʿ ʰ ֽϴ.

 

 

 

Linear Mixed Model Assumption

 

Linear mixed model ϴ.

 

Random effects 0̰ л G R Ժ .

▪ Random effects ̴.

() ̴.

 

 


 

Toy

Define the Mixed Model

 

տ Ǿ Toy mixed model 캸ڽϴ.


fixed effects(ȿ) Ű 4 Դϴ. (ü + 3 )

random effects Ű 7 (7(blocks)) ̹Ƿ, 3x7=21 ġ ǰ,

ġ شϴ 21 random errors մϴ.

 

fixed effects(X) random effects(Z) mixed model Ʒ ˴ϴ.

 

 

 

 

 

 

 

Covariance Matrices

 

Random effect Ϳ random error л-л İ ׿ y л-л Ʒ ˴ϴ.

 

 

 

 

 

     è     

 

 

 

 



Ʒ Ǿ ֽϴ.


 

 

 

 

 

 

 

[ó]

 

- Applied Mixed Models for Processors Course Notes

 

 

 

 

 


 

 
 
 
 
 [Mixed Model 1.5.2] Introduction to the Theory of General Linear Mixed Models
 [Mixed Model 1.4.2] Using the MIXED Procedure