model1 <- '
    Yi ~ ai*X1i + bi*X2i
    Yj ~ aj*X1j + bj*X2j
    Yi~~Yj
    adiff := aj - ai
    bdiff := bj - bi'
fit1 <- sem(model1, data = data)
summary(fit1)

model2 <- '
    Yi ~ a*X1i + b*X2i
    Yj ~ a*X1j + b*X2j
    Yi~~Yj'
fit2 <- sem(model2, data = data)
summary(fit2)

lavTestLRT(fit2, fit1)