! K2. Phenotypic Assortment Model
! Rose Fear Data

Group 1: Mother-Father covariance
!  RpDRp
Data Calculation NGroups=12
Matrices
D Full 1 1 free    ! assortative mating delta paths
P Symm 1 1 free    ! within person covariance (Rp)
Compute  P*D*P /
Start 1.0 P 1 1
Option No_output
End

Group 2: Calculate T   Genotype-Phenotype covariance
!  T = a'Ra+c's
Data Calculation
Matrices
A Low  1 1 free    ! additive genetic paths
C Low  1 1 free    ! common environment paths
G Symm 1 1 free    ! additive genetic covariance (Ra)
S Full 1 1 free    ! A-C covariance
Compute  G*A' + S*C' /
Start 1.0 G 1 1 
Start  .5 A 1 1
Start  .5 C 1 1
Option No_output
End

Group 3: Mother-Child covariance
!  (Rpm'+Wf')c' + (1+RpDT')(.5a')
Data Calculation
Matrices
A Low  1 1 =A2     ! additive genetic paths
C Low  1 1 =C2     ! common environment paths
D Full 1 1 =D1     ! assortative mating delta paths 
F Full 1 1 free    ! paternal cultural transmission
H Full 1 1         ! scalar, .5
I Iden 1 1         ! identity matrix
M Full 1 1 free    ! maternal cultural transmission
P Symm 1 1 =P1     ! within person covariance (Rp)
T Full 1 1 =%E2    ! A-P covariance
W Full 1 1 =%E1    ! spouse covariance
Compute  (P*M' + W*F')*C' + (I + P*D)*T'*(H@A') /
Matrix H 0.5
End

Group 4: Father-Child Covariance
!  (Rpf'+Wm')c' + (1+RpDT')(.5a')
Data Calculation
Matrices
A Low  1 1 =A2     ! additive genetic paths
C Low  1 1 =C2     ! common environment paths
D Full 1 1 =D1     ! assortative mating delta paths 
F Full 1 1 =F3     ! paternal cultural transmission
H Full 1 1 =H3     ! scalar .5
I Iden 1 1         ! identity matrix
M Full 1 1 =M3     ! maternal cultural transmission
P Symm 1 1 =P1     ! within person covariance (Rp)
T Full 1 1 =%E2    ! A-P covariance
W Full 1 1 =%E1    ! spouse covariance
Compute  (P*F' + W'*M')*C' + (I + P*D')*T'*(H@A') /
Option No_output
End

Group 5:  MZ Twin Covariance
!  aRaa' + cRcc' + asc' + cs'a' + nn' 
Data Calculation
Matrices
A Low  1 1 =A2     ! additive genetic paths
C Low  1 1 =C2     ! common environment paths
G Symm 1 1 =G2     ! additive genetic covariance (Ra)
N Low  1 1         ! non-additive paths
R Symm 1 1 free    ! common environment covariance (Rc)
S Full 1 1 =S2     ! A-C covariance
Compute  A*G*A' + C*R*C' +A*S*C' + C*S'*A' + N*N' /
Start 1.0 R 1 1
End

Group 6:  DZ Twin Covariance
!  .5a(Ra+.5(T(D'+D)T'))a' + cRcc' + asc' + cs'a' + .25nn'
Data Calculation
Matrices
A Low  1 1 =A2     ! additive genetic paths
C Low  1 1 =C2     ! common environment paths
D Full 1 1 =D1     ! assortative mating delta paths
G Symm 1 1 =G2     ! additive genetic covariance (Ra)
H Full 1 1 =H3     ! scalar, .5
N Low  1 1 =N5     ! non-additive paths
R Symm 1 1 =R5     ! common environment covariance (Rc)
S Full 1 1 =S2     ! A-C covariance
T Full 1 1 =%E2    ! A-P covariance
Compute  H@A*(G + H@(T*(D'+D)*T'))*A' + C*R*C' +A*S*C' + C*S'*A' +H@H@N*N'/
Option No_output
End

Group 7:  Genetic Constraint
!  Ra = .5@(Ra+.5@(T(D'+D)T')+1)
Data Constraint NInput=1
Matrices
D Full 1 1 =D1     ! assortative mating delta paths
G Symm 1 1 =G2     ! additive genetic covariance (Ra)
H Full 1 1 =H3     ! scalar, .5
I Iden 1 1         ! segregation variance, .5I
T Full 1 1 =%E2    ! A-P covariance
Constraint  G - (H@(G + H@(T*(D'+D)*T') + I)) /
Option Rsidual
End

Group 8:  A-C Constraint 
!  s = .5(T(m'+f'+DRpm'+DRpf'))
Data Constraint NInput=1 
Matrices
D Full 1 1 =D1     ! assortative mating delta paths
F Full 1 1 =F3     ! paternal cultural transmission
H Full 1 1 =H3     ! scalar, .5
M Full 1 1 =M3     ! maternal cultural transmission
P Symm 1 1 =P1     ! within person covariance (Rp)
S Full 1 1 =S2     ! A-C covariance
T Full 1 1 =%E2    ! A-P covariance
Constraint   S - (H@T*(M' + F' + D*P*M' + D'*P*F')) /
Option Rsidual
End

Group 9: Common Environment Constraint
!  Rc = mPm'+fPf'+mWf'+fW'm'+1
Data Constraint NInput=1
Matrices
B Iden 1 1         ! common environment residual variance
F Full 1 1 =F3     ! paternal cultural transmission
M Full 1 1 =M3     ! maternal cultural transmission
P Symm 1 1 =P1     ! within person covariance
R Symm 1 1 =R5     ! common environment covariance (Rc)
W Full 1 1 =%E1    ! spouse covariance
Constraint R - (M*P*M' + F*P*F' + M*W*F' + F*W'*M' + B) /
Option Rsidual
End

Group 10: Phenotypic Variance Constraint
!  Rp = aRaa + cRcc' + asc' + cs'a' + nn' + ee'
Data Constraint NInput=1
Matrices
A Low  1 1 =A2     ! additive genetic paths
C Low  1 1 =C2     ! common environment paths
G Symm 1 1 =G2     ! additive genetic covariance (Ra)
J Low  1 1 free    ! specific environment paths
N Low  1 1 =N5     ! non-additive paths
P Symm 1 1 =P1     ! within person covariance (Rp)
R Symm 1 1 =R5     ! common environment covariance
S Full 1 1 =S2     ! A-C covariance
Constraint P - (A*G*A' + C*R*C' + J*J'+ A*S*C' + C*S'*A' + N*N') /
Start .707 J 1 1 
Option Rsidual
End

Group 11 - MZ Twins and parents  Rose Fear Factor 1 
DA NInput=4 NObservations=144
Labels
DAD_1 MOM_1 T1_1 T2_1 
CMatrix
.90
.11 1.11
.25 .09 .95
.16 .21 .49 .89
Matrices
A Full 1 1 =%E3    ! Mother-child covariances
B Full 1 1 =%E4    ! Father-child covariances
C Full 1 1 =%E5    ! MZ twin covariances
D Full 1 1 =%E1    ! Spouse covariances
E Symm 1 1 =P1     ! Within person covariances
Covariance ( E | D'| B | B )_
           ( D | E | A | A )_
           ( B'| A'| E | C )_
           ( B'| A'| C'| E )   /
Option rs
End

Group 12 - DZ twins and parents  Rose Fear Factor 1 
Data NInput=4 NObservations=106
Labels
DAD_1 MOM_1 T1_1 T2_1 
CMatrix
1.08
.21 .91
.14 .24 1.21
.10 .16 .32 1.03
Matrices
A Full 1 1 =%E3    ! Mother-child covariances
B Full 1 1 =%E4    ! Father-child covariances
C Full 1 1 =%E6    ! DZ twin covariances
D Full 1 1 =%E1    ! Spouse covariances
E Symm 1 1 =P1     ! Within person covariances
Covariance ( E | D'| B | B )_
           ( D | E | A | A )_
           ( B'| A'| E | C )_
           ( B'| A'| C'| E )   /
Option Rsidual IT=800
End