Supplemental Materials For Psychological Methods Website
LISREL Syntax For Fitting the Unconstrained, Constrained and GAPI Approaches with 3-matched Product Indicators
Unconstrained Approach
Unconstrained 3-match
X- observed variables have been centered
ML estimation
DA NI=12 NO=500
RA FI=int.dat
LA
y1 y2 y3 x1 x2 x3 x4 x5 x6 x1x4 x2x5 x3x6 ! x1x4, x2x5, x3x6 are indicators of the latent interaction factor
MO NY=3 NE=1 NX=9 NK=3 LY=FU,FI LX=FU,FI PS=SY,FR PH=SY,FR TE=DI,FR TD=DI,FR KA=FR TY=FR
! FI PH 3 1 PH 3 2 ! can be used for known normally distributed KSI1, KSI2
! ST 0 PH 3 1 PH 3 2 ! can be used for known normally distributed KSI1, KSI2
VA 1 LY 1 1
FR LY 2 1 LY 3 1
VA 1 LX 1 1 LX 4 2 LX 7 3
FR LX 2 1 LX 3 1 LX 5 2 LX 6 2 LX 8 3 LX 9 3
FR GA 1 1 GA 1 2 GA 1 3
FI KA(1) KA(2)
VA 0 KA(1) KA(2) ! see Equation (2)
CO KA(3)=PH(2,1) ! see Equation (2)
OU ND=6 AD=off EP=0.0001 IT=500 XM
Constrained Approach
Constrained 3-match
X- observed variables have been centered
ML estimation
DA NI=12 NO=500
RA FI=int.dat
LA
y1 y2 y3 x1 x2 x3 x4 x5 x6 x1x4 x2x5 x3x6
MO NY=3 NE=1 NX=9 NK=3 LY=FU,FI LX=FU,FI PS=SY,FR PH=SY,FR TE=DI,FR TD=DI,FR KA=FR TY=FR
FI PH 3 1 PH 3 2
ST 0 PH 3 1 PH 3 2
VA 1 LY 1 1
FR LY 2 1 LY 3 1
VA 1 LX 1 1 LX 4 2 LX 7 3
FR LX 2 1 LX 3 1 LX 5 2 LX 6 2 LX 8 3 LX 9 3
FR GA 1 1 GA 1 2 GA 1 3
FI KA(1) KA(2)
VA 0 KA(1) KA(2) ! see Equation (2)
CO KA(3)=PH(2,1) ! see Equation (2)
!the unconstrained approach does not include the following set of constraints
CO LX 8,3 = LX 2 1 * LX 5 2
CO LX 9,3 = LX 3 1 * LX 6 2
CO PH 3 3 = PH(1,1)*PH(2,2)+ PH(2,1)** 2 !the GAPI approach does not include this constraint
CO TD 7 7 = PH(1,1)*TD(4,4)+ PH(2,2)*TD(1,1)+TD(1,1)*TD(4,4)
CO TD 8 8 = LX(2,1)**2*PH(1,1)*TD(5,5)+ LX(5,2)**2*PH(2,2)*TD(2,2)+TD(2,2)*TD(5,5)
CO TD 9 9 = LX(3,1)**2*PH(1,1)*TD(6,6)+ LX(6,2)**2*PH(2,2)*TD(3,3)+TD(3,3)*TD(6,6)
OU ND=6 AD=off EP=0.0001 IT=500 xm
GAPI Approach
GAPI 3-match
X- observed variables have been centered
ML estimation
DA NI=12 NO=500
RA FI=int.dat
LA
y1 y2 y3 x1 x2 x3 x4 x5 x6 x1x4 x2x5 x3x6
MO NY=3 NE=1 NX=9 NK=3 LY=FU,FI LX=FU,FI PS=SY,FR PH=SY,FR TE=DI,FR TD=DI,FR KA=FR TY=FR
VA 1 LY 1 1
FR LY 2 1 LY 3 1
VA 1 LX 1 1 LX 4 2 LX 7 3
FR LX 2 1 LX 3 1 LX 5 2 LX 6 2 LX 8 3 LX 9 3
FR GA 1 1 GA 1 2 GA 1 3
FI KA(1) KA(2)
VA 0 KA(1) KA(2) ! see Equation (2)
CO KA(3)=PH(2,1) ! see Equation (2)
! except for one constraint not used in GAPI, the following are identical to those in the constrained approach
CO LX 8,3 = LX 2 1 * LX 5 2
CO LX 9,3 = LX 3 1 * LX 6 2
CO TD 7 7 = PH(1,1)*TD(4,4)+ PH(2,2)*TD(1,1)+TD(1,1)*TD(4,4)
CO TD 8 8 = LX(2,1)**2*PH(1,1)*TD(5,5)+ LX(5,2)**2*PH(2,2)*TD(2,2)+TD(2,2)*TD(5,5)
CO TD 9 9 = LX(3,1)**2*PH(1,1)*TD(6,6)+ LX(6,2)**2*PH(2,2)*TD(3,3)+TD(3,3)*TD(6,6)
OU ND=6 AD=off EP=0.0001 IT=500 xm