#
# Interaction as per Jaccard and Wen (1995)
#
# From Li et al. in MBR 33(1), 1-39, 1998
#
# cross1 <- peou1*pu1
# cross2 <- peou1*pu2
# cross3 <- peou2*pu1
# cross4 <- peou2*pu2
#
# Define standard reflective latents and label the loading and error variance params
#
iu =~ iu1 + iu2
#
peou =~ peou1 + l1*peou2
peou1 ~~ t1*peou1
peou2 ~~ t2*peou2
#
pu =~ pu1 + l2*pu2
pu1 ~~ t3*pu1
pu2 ~~ t4*pu2
#
# Interaction term
#
cross =~ cross1 + l3*cross2 + l4*cross3 + l5*cross4
cross1 ~~ t5*cross1
cross2 ~~ t6*cross2
cross3 ~~ t7*cross3
cross4 ~~ t8*cross4
cross1 ~~ cross2
cross1 ~~ cross3
# cross1 ~~ cross4
# cross2 ~~ cross3
cross2 ~~ cross4
cross3 ~~ cross4
#
# Setup covariances of exogenous latents and label them
#
peou ~~ p1*peou
pu ~~ p2*pu
peou ~~ p12*pu
peou ~~ 0*cross
pu ~~ 0*cross
cross ~~ p3*cross
#
# Model additional constraints
#
# Loadings
#
l3 == l2
l4 == l1
l5 == l1*l2
#
# Latent variances
#
p3 == p1*p2+p12*p12
#
# Error variances
#
t5 == p1*t3 + p2*t1 + t1*t3
t6 == p1*t4 + l2*l2*p2*t1 + t1*t4
t7 == l1*l1*p1*t3 + p2*t2 + t2*t3
t8 == l1*l1*p1*t4 + l2*l2*p2*t2 + t2*t4
#
# Regressions
#
iu ~ peou + pu + cross
#
