I am estimating a model with two simultaneous equations, one for Y and one for X, and each equation includes unique predictors. Y on lagY X lagX z1 z2 z3 X on lagX M lagM z1 z2 z4 I am looking at how parental support (X) affects youth occupational status (Y). I have repeated measures for X and Y and I want to tackle simultaneity, as Y may also affect X. z1 and z2 are socio-demographic variables. z3 is unique in the equation for Y (occupational status) and represents business cycle effects. z4 is unique in the equation for X (parental support) and represents the number of siblings. My panel is unbalanced, with respondents followed up to 4 times. Data are in long format. I use Cluster is pid and type=complex.
There is no feedback loop in the model as in the equation for X (parental support) I use M (employment status) as predictor, and not Y (occupational status).
While the model above includes lagged and contemporaneous effects, theoretically I would justify a simpler model including only the lagged effect of X and Y and only the contemporaneous effect of M on X, which would read Y on lagY lagX z1 z2 z3 X on lagX M z1 z2 z4. The latter model gives MSEA=0.03, CFI=0.96; TLI=0.80.
I wonder whether this all makes sense and whether I need to perform additional tests. I am very new to SEM and MPlus and any feedback is highly appreciated. Thank you so much.