Path analysis for reciprocal relation... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 ecl posted on Wednesday, February 04, 2009 - 6:15 pm
I have two observed variables measured at 4 time points. I want to use an auto-regressive cross-lag model with contemporaneous effects to investigate the reciprocal relationship between these variables. Can you suggest any examples for how to do this using Mplus?
 Linda K. Muthen posted on Wednesday, February 04, 2009 - 9:45 pm
You would use the ON option to specify this model, for example,

y4 ON y3; y3 ON y2; y2 ON y1;
z4 ON z3; z3 ON z2; z2 ON z1;

y4 ON z3;
z4 ON y3;

y2 ON z2;
z2 ON y2;

I'm not sure exactly how you want to specify your model but those are the basic building blocks. I'm not sure about identification.
 ecl posted on Friday, February 13, 2009 - 9:13 pm
To build upon my past question, I essentially want to have 2 repeated measures models with random intercepts for the 2 variables measured across the 4 time points(i.e. a repeated measures model for y1 y2 y3 y4 and a repeated measures model for z1 z2 z3 z4). I also want to include cross-lagged paths between the variables (i.e. y2 on z1, y3 on z2, y4 on z3, z2 on y1, z3 on y2, z4 on y3) and correlation between the random intercepts. Will this work with Mplus, and if so, how would I go about specifying it?
 Linda K. Muthen posted on Sunday, February 15, 2009 - 4:52 pm
It sounds like you want a hybrid model. Start with Example 6.1 and add the ON statements that you want.
 Natalie posted on Tuesday, February 23, 2010 - 8:52 pm

I have a similar model to the one described above. It has two repeated measures that were collected at three time points. I've presented a model with cross-lagged paths between T1 and T2 and between T2 and T3, as well as the auto-regressive paths from T1 to T2 and T2 to T3. A reviewer would like me to add in autoregressive paths for both variables from T1 to T3, as well as cross lagged paths from T1 to T3. Is there any reason I would want to do this? Note that my measures are at least moderately stable across time (standardized betas > .55 for each auto-regressive path).

Thank you!
 Linda K. Muthen posted on Tuesday, February 23, 2010 - 10:24 pm
I don't know if there is any reason but you might add the paths to the model and see what happens. Perhaps some evidence for an argument one way or the other will show up.
 Jahun Kim posted on Thursday, June 23, 2011 - 3:58 am
Dear Dr. Muthen,

I have two (observed) variables measured two time points. I'd like to examine reciprocal relationship between these two variables with cross-lagged model.
I build up my model based on your posted answer this page. In the output, Chi-square is 0, RMSEA is 0, and CFI is 1.00.

Could you take a look at my input?




q3p_dep on q1p_dep;
q4psupp on q2psupp;

q4psupp on q1p_dep;
q3p_dep on q2psupp;
 Linda K. Muthen posted on Thursday, June 23, 2011 - 5:30 pm
This looks correct. The model has no degrees of freedom. Model fit cannot be assessed.
 Jahun Kim posted on Thursday, June 23, 2011 - 5:36 pm
Thank you Linda.
 Eric Thibodeau posted on Sunday, March 08, 2015 - 9:17 pm

I'm trying to run a cross sectional SEM with a reciprocal paths between two observed variables.

For example:

f1 by in1 in2 in3 in4;

f1on X Y M;
X on Y;
Y on X M;

Do I need to specify a covariance between X and Y disturbances? If so how do I do that? Thanks!
 Linda K. Muthen posted on Sunday, March 08, 2015 - 10:35 pm
In a reciprocal interaction, each dependent variable must have a unique predictor. Y has m but x does not have a unique predictor.
 Anna Manzoni posted on Friday, June 26, 2015 - 3:49 pm
I am interested in 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.
My panel is unbalanced, with respondents followed up to 4 times. Data are in long format. I use Cluster is pid and type=complex.
My model now has cross-lagged and cross-contemporaneous effects, plus control variables and a unique predictor for each equation (z3 for Y; z4 for X).
Y on X lagX lagY z1 z2 z3
X on Y lagY lagX z1 z2 z4
1.Which conditions should the unique predictors satisfy and how to test that in MPlus?
2.Should I include correlation btw lagX and lagY?
Alternatively I could have the lagged “employment rate”( M below) rather than the lagged occupational status (lagY) in the equation for X, which would make the model “pseudo”non-recursive, with no actual feedback loop.
Y on X lagX lagY z1 z2
X on M lagM lagX z1 z2
3. Would I still need z3 and z4 as unique predictors or I may be able to consider a lagged variable as an instrument?
I wonder whether this makes sense and is correctly specified. In particular I wonder about
a. the use of lagged dep and indep variables
b. the presence of cross-contemporaneous and cross-lagged effects
c. the need for instrumental variables and how to test their validity in MPlus
Thank you.
 Bengt O. Muthen posted on Saturday, June 27, 2015 - 10:36 pm
I think you can get good feedback on these more general analysis questions on SEMNET.
 Anna Manzoni posted on Wednesday, July 01, 2015 - 1:07 am
Thank you. I had tried that already, but no luck :-(
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