G1 CALCULATION GROUP control Correlation matrix A factor 
DA CALC NG=8
MATRICES 
A Lo 1 1 Fixed 
C Lo 1 1 Free 
H Fu 1 1
I id 1 1 
begin algebra; 
X = A*A' ; 
Y = C*C' ; 
end algebra; 
COMPUTE I|H@X+Y_ 
        H@X+Y|I;
Matrix A 0
Matrix H .5
Option RS 
End 

G2 CALCULATION GROUP clinical Correlation matrix A factor 
DA CALC 
MATRICES 
A Lo 1 1 =A1 
C Lo 1 1 =C1 
H fu 1 1 
I id 1 1 
begin algebra; 
X = A*A' ; 
Y = C*C' ; 
end algebra ; 
COMPUTE I|H@X+Y_ 
        H@X+Y|I ; 
Matrix H .5 
Option RS 
End 

G3 CALCULATION GROUP control Correlation matrix AB factor 
DA CALC 
MATRICES 
A Lo 1 1 Fixed 
C Lo 1 1 Free 
H Fu 1 1
I id 1 1 
begin algebra; 
X = A*A' ; 
Y = C*C' ; 
end algebra; 
COMPUTE I|H@X+Y_ 
        H@X+Y|I;
Matrix A 0
Matrix H .5
Option RS 
End 

G4 CALCULATION GROUP clinical Correlation matrix AB factor 
DA CALC 
MATRICES 
A Lo 1 1 =A3 
C Lo 1 1 =C3 
H fu 1 1 
I id 1 1 
begin algebra; 
X = A*A' ; 
Y = C*C' ; 
end algebra ; 
COMPUTE I|H@X+Y_ 
       H@X+Y|I ; 
Matrix H .5 
Option RS 
End 

G5 CALCULATION GROUP control Correlation matrix B factor 
DA CALC 
MATRICES 
A Lo 1 1 Fixed 
C Lo 1 1 Free 
H Fu 1 1
I id 1 1 
begin algebra; 
X = A*A' ; 
Y = C*C' ; 
end algebra; 
COMPUTE I|H@X+Y_ 
        H@X+Y|I;
Matrix A 0
Matrix H .5
Option RS 
End 

G6 CALCULATION GROUP clinical Correlation matrix B factor 
DA CALC 
MATRICES 
A Lo 1 1 =A5 
C Lo 1 1 =C5 
H fu 1 1 
I id 1 1 
begin algebra; 
X = A*A' ; 
Y = C*C' ; 
end algebra ; 
COMPUTE I|H@X+Y_ 
        H@X+Y|I ; 
Matrix H .5 
Option RS 
End 

Three disorders model - attempt parameter recovery 
Data NI=6
ordinal fi=control.dat
Labels age1 age2 sex1 sex2 type dummy
Definition_variables age1 age2 sex1 sex2 type /
Matrices 
A Full 2 2 =%E1 ! corr between A factors 
C Full 2 2 =%E3 ! corr between AB factors 
B Full 2 2 =%E5 ! corr between B factors 
D Full 1 2 ! Matrix for age Sibling 1& Sibling 2
E Full 1 2 ! Matrix for sex Sibling 1 & Sibling 2
P Full 1 2 ! Threshold for A 
Q Full 1 2 ! Age difference in threshold for A
N Full 1 2 ! Sex difference in threshold for A
R Full 1 2 ! Threshold for AB 
T Full 1 2 ! Age difference for threshold for AB
I Full 1 2 ! Sex difference in threshold for AB
U Full 1 2 ! Threshold for B
V Full 1 2 ! Age difference for threshold for B
M Full 1 2 ! Sex difference for threshold for B 
K Full 1 1 ! variance of dummy variable
L Full 4 1 !  for extracting right part of S 
W Full 1 1 ! 0 + + These are to control integral type 
Z Full 1 1 ! 1 - - 
Begin Algebra; 
! (P+(D.Q)+(E.N)) ! threshold for A 
! (R+(D.T)+(E.I))  ! threshold for AB
! (U+(D.V)+(E.M))  ! threshold for B
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))) ; !lower/lower for A
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))) ; !lower/upper for A
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))) ; !upper/lower for A
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))) ; !upper/upper for A
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))) ; !lower/lower for AB
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))) ; !lower/upper for AB
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))) ; !upper/lower for AB
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|W))) ; !upper/upper for AB
F = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_Z|Z))) ; !lower/lower for B
G = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_Z|W))) ; !lower/upper for B
H = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_W|Z))) ; !upper/lower for B
J = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_W|W))) ; !upper/upper for B
Y = \muln(Z_(P+(D.Q)+(E.N))'_Z) ; ! below threshold on A 
O = \muln(Z_(U+(D.V)+(E.M))'_Z) ; ! below threshold on B 
! (Z-Y)   ! above threshold on A
! (Z-O)   ! above threshold on B
S = 	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).F_  	! 1 (expected probability of 0000)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H_ 		! 2 (expected probability of 0100)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).G_ 		! 3 (expected probability of 0001)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).F_ 		! 4 (expected probability of 1000)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).F_ 		! 5 (expected probability of 0010)
	Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).O + 									
		(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H_ 	! 6 (expected probability of 1100)	
	Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).O +									
		(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).G_ 	! 7 (expected probability of 0011)	
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J_ 		! 8 (expected probability of 0101)		 
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).G_ 		! 9 (expected probability of 1001)		 
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H_  	! 10 (expected probability of 0110)		 
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J +			 
		Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).(Z-O)_               					! 11 (expected probability of 1101)					 
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J +			 
		Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).(Z-O)_               					! 12 (expected probability of 0111)					 
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).F_    	! 13 (expected probability of 1010)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).O_								! 14 (expected probability of 1110)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).G +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).O_								! 15 (expected probability of 1011)
	(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).(Z-O) +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).(Z-O) +
		(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|W)));									! 16 (expected probability of 1111)
end algebra; 
Matrix L 1 1 1 1 
Matrix K .159154943
Matrix W 0
Matrix Z 1
Specify P 100 100
Specify Q 101 101
Specify N 102 102
Specify R 103 103
Specify T 104 104
Specify I 105 105
Specify U 106 106  
Specify V 107 107
Specify M 108 108
!Start .6 all 
Matrix P 2 2 
Matrix R 2 2 
Matrix U 2 2  
Specify D age1 age2;
Specify E sex1 sex2;
Specify L -5 0 -5 0;
Means W;
Covariance K;
Weight (\part(S,L)) /
!Option RS User-def
Option RS
End 

Three disorders model - clinical data 
Data NI=6
ordinal fi=clinical.dat
Labels age1 age2 sex1 sex2 type dummy
Definition_variables age1 age2 sex1 sex2 type /
Matrices 
A Full 2 2 =%E2 ! corr between A factors 
C Full 2 2 =%E4 ! corr between AB factors 
B Full 2 2 =%E6 ! corr between B factors 
D Full 1 2 ! Matrix for age Sibling 1& Sibling 2
E Full 1 2 ! Matrix for sex Sibling 1 & Sibling 2
P Full 1 2 =P7 ! Threshold for A 
Q Full 1 2 =Q7! Age difference in threshold for A
N Full 1 2 =N7! Sex difference in threshold for A
R Full 1 2 =R7! Threshold for AB 
T Full 1 2 =T7! Age difference for threshold for AB
I Full 1 2 =I7! Sex difference in threshold for AB
U Full 1 2 =U7! Threshold for B
V Full 1 2 =V7! Age difference for threshold for B
M Full 1 2 =M7! Sex difference for threshold for B 
K Full 1 1 ! variance of dummy variable
L Full 4 1 !  for extracting right part of S 
W Full 1 1 ! 0 + + These are to control integral type 
Z Full 1 1 ! 1 - - ! also ascertainment parameter for illicit drug dependence (fixed to 1)
X Full 1 1 free ! ascertainment parameter for alcohol dependence
Begin Algebra; 
! (P+(D.Q)+(E.N)) ! threshold for A 
! (R+(D.T)+(E.I))  ! threshold for AB
! (U+(D.V)+(E.M))  ! threshold for B
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))) ; !lower/lower for A
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))) ; !lower/upper for A
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))) ; !upper/lower for A
! (\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))) ;  !upper/upper for A
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))) ;  !lower/lower for AB
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))) ;  !lower/upper for AB
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))) ;  !upper/lower for AB
! (\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|W))) ;  !upper/upper for AB
F = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_Z|Z))) ;  !lower/lower for B
G = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_Z|W))) ;  !lower/upper for B
H = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_W|Z))) ;  !upper/lower for B
J = (\muln((B_(U+(D.V)+(E.M))_(U+(D.V)+(E.M))_W|W))) ;  !upper/upper for B
Y = \muln(Z_(P+(D.Q)+(E.N))'_Z) ; ! below threshold on A 
O = \muln(Z_(U+(D.V)+(E.M))'_Z) ; ! below threshold on B 
! (Z-Y)   ! above threshold on A
! (Z-O)   ! above threshold on B
S =  
	(z).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H)_ 		! 2 (expected probability of 0100)
	(x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).F)_ 		! 4 (expected probability of 1000)
	(z+x).(Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).O + 									
		(\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H)_ 	! 6 (expected probability of 1100)		
	(z).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J)_ 		! 8 (expected probability of 0101)			
	(x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).G)_ 		! 9 (expected probability of 1001)			 
	(z).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H)_  	! 10 (expected probability of 0110)		 
	(z+x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|Z))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J +			 
		Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).(Z-O))_               						! 11 (expected probability of 1101)						 
	(z).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_Z|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J +			 
		Y.(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).(Z-O))_               						! 12 (expected probability of 0111)						 
	(x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).F)_    	! 13 (expected probability of 1010)		 
	(z+x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).H +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).O)_									! 14 (expected probability of 1110)
	(x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).G +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).O)_									! 15 (expected probability of 1011)
	(z+x).((\muln((A_(P+(D.Q)+(E.N))_(P+(D.Q)+(E.N))_W|W))).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|Z))).J +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|Z))).(Z-O) +
		(Z-Y).(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_Z|W))).(Z-O) +
		(\muln((C_(R+(D.T)+(E.I))_(R+(D.T)+(E.I))_W|W))));										! 16 (expected probability of 1111)
end algebra; 
Matrix L 1 1 1 1 
Matrix K .159154943
Matrix W 0
Matrix Z 1
Matrix X .5
Specify D age1 age2;
Specify E sex1 sex2;
Specify L -5 0 -5 0;
Means W;
Covariance K;
Weight (\part((S%( \sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S)_\sum(S))),L)) /
Option Th=-3
Option RS
End