MX script for a univariate GxE QTL model from Chapter 11

!GxE QTL model with two moderator variables 

#define nmod 3 ! unmod, yob, sex
#define ndef 2 ! nmod -1 
#define nsib 4 ! size of largest sibship
#define sib 3 ! nsib-1

Data Calc NGroups=3
Begin Matrices ;
 A full 1 nmod free      
 ! this matrix will hold estimates of: the unmoderated, YOB moderated and Sex 
 ! moderated Additive genetic path coefficients
 C full 1 nmod free
 ! this matrix will hold estimates of: the unmoderated, YOB moderated and Sex 
 ! moderated Common environmental path coefficients
 E full 1 nmod free
 ! this matrix will hold estimates of: the unmoderated, YOB moderated and Sex 
 ! moderated Unique environmental path coefficients
 Q full 1 nmod free
 ! this matrix will hold estimates of: the unmoderated, YOB moderated and Sex 
 ! moderated QTL path coefficients
 M full 1 1 free	      ! mean
 B full 1 ndef free       ! mean effects
 H Stand nsib nsib         ! mz constants
 J Stand nsib nsib         ! dz constants
 U unit nsib 1
 D diag nsib nsib 
End Matrices ;

Value 1 H 2 1
Value .5 H 3 1 to H sib sib
Value .5 H 2 1 to H sib sib
Start 0 M 1 1 
Start 1 d 1 1 d 2 2 d 3 3 d 4 4 

 Labels column A unmod yob sex
 Labels column C unmod yob sex
 Labels column E unmod yob sex
 Labels column B yob sq bw sex
 Options RSiduals
End

G2: MZ Data group
Data NInput=17
Rectangular File=mz.dat
labels 
 phenotype1 phenotype2 phenotype3 phenotype4 
 yob1 yob2 yob3 yob4
 sex1 sex2 sex3 sex4
 pab pac pbc pad pbd pcd

Select phenotype1 phenotype2 phenotype3 phenotype4 yob1 yob2 yob3 yob4 sex1 sex2 sex3 sex4 pab pac pbc pad pbd pcd;
Definition_variables yob1 yob2 yob3 yob4 sex1 sex2 sex3 sex4 pab pac pbc pad pbd pcd;

Matrices =Group 1
 V full nmod nsib   ! covariates for variance effects
 W full ndef nsib   ! covariates for mean effects
 P stand nsib nsib  ! to contain pihats
End Matrices ;

!place yob in the 2nd row of the v matrix and sex in the 3rd
!the 1st row contains 1s for the unmoderated variance components
!this matrix will be * multiplied to produce variance components that include 
!the GxE effects
Specify V
  0 0 0 0
  yob1 yob2 yob3 yob4
  sex1 sex2 sex3 sex4
Value 1 V 1 1 V 1 2 v 1 3 v 1 4

!place yob in the 1st row of the w matrix and sex in the 2nd
Specify W
  yob1 yob2 yob3 yob4
  sex1 sex2 sex3 sex4

!place the pihats in the P matrix in the correct order
Specify P 
 pab 
 pac pbc 
 pad pbd pcd;

Means (U@M) + (B*W) ;
Covariance 	 
(H.((U@A)*V).(V'*(U@A)'))+     !additve genetic effects
((U@C)*V).(V'*(U@C)')+         !common environmental effects
(P.((U@Q)*V).(V'*(U@Q)'))+         !qtl effects
(D.((U@E)*V).(V'*(U@E)')) ;    !unique environmental effects

End
 
G3: DZ
Data NInput=17
Rectangular File=mz.dat
Labels
 phenotype1 phenotype2 phenotype3 phenotype4 
 yob1 yob2 yob3 yob4
 sex1 sex2 sex3 sex4
 pab pac pbc pad pbd pcd

Select phenotype1 phenotype2 phenotype3 phenotype4 yob1 yob2 yob3 yob4 sex1 sex2 sex3 sex4 pab pac pbc pad pbd pcd;
Definition_variables yob1 yob2 yob3 yob4 sex1 sex2 sex3 sex4 pab pac pbc pad pbd pcd;

Matrices =Group 1
 V full nmod nsib   ! covariates for variance effects
 W full ndef nsib   ! covariates for mean effects
 P stand nsib nsib  ! to contain pihats
End Matrices ;

!place yob in the 2nd row of the v matrix and sex in the 3rd
!the 1st row contains 1s for the unmoderated variance components
Specify V
  0 0 0 0
  yob1 yob2 yob3 yob4
  sex1 sex2 sex3 sex4
Value 1 V 1 1 V 1 2 v 1 3 v 1 4

!place yob in the 1st row of the w matrix and sex in the 2nd
Specify W
  yob1 yob2 yob3 yob4
  sex1 sex2 sex3 sex4

Specify P 
 pab 
 pac pbc 
 pad pbd pcd;

Means (U@M) + (B*W) ;
Covariance 	 
(J.((U@A)*V).(V'*(U@A)'))+     !additve genetic effects
((U@C)*V).(V'*(U@C)')+         !common environmental effects
(P.((U@Q)*V).(V'*(U@Q)'))+         !qtl effects
(D.((U@E)*V).(V'*(U@E)')) ;    !unique environmental effects

 Option multiple

End

save temp.mxs
!test the QTLxSex effect
Drop Q 1 1 3
End

get temp.mxs
!test the QTLxYOB effect
Drop Q 1 1 2
End

!test both the QTLxSex and QTLxYOB effects
Drop Q 1 1 3
End

!test the unmoderated QTL effect
Drop Q 1 1 1
End