This is my input in mplus. When I run the model, the program did not work and give output as usual. It calculated the model but not give the results of specific indirect effects. I also do not know that my model is available to analyze a reciprocal relationship.
ANALYSIS: TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 1000;
! Direct effects;
MODEL: X on Y Z M C;
B on X M F;
C on B X;
A on S X B M C;
! Correlations;
Y with Z;
M with Z;
Y with M;
X with C;
! Control variables;
C on grade s1_3 Gender;
A on grade s1_3 Gender;
!Indirect effects;
MODEL INDIRECT: A ind Y;
A ind Z;
A ind M;
A ind X;
OUTPUT: SAMPSTAT Stdyx CINTERVAL(BCBOOTSTRAP);
Your model is non-recursive (path X --> C and C --> X and correlated disturbances X with C). There may be an identification problem. Bollen (1989, Structural Equations with Latent Variables, Wiley) discusses identification for non-recursive path models.
Dear Geiser, thank you so much for your answer and book suggestion.
Hello Ezgi,
basically, as Christian said, the feedback loop is not easily identified. You need further variables called instruments that have only effects of one of the variables. For instance, if you have two variables X and Y supposedly causing each others, you need at least a variable w1 that only affects X and w2 that affects Y (but not cross-effects (these "exclusion restrictions" are part of the overall chi-square test). If this holds you can estimate the feedback loop. You can then either estimate the error covariance between X and Y from the start or fix it to zero and test whether the model fits. If there are unobserved confounders affecting both then the model will not fit. Hence, your overall chi-square test tests all implications (fixed-to-zero effecs and fixed error covariance) in one step.
Here are some paper that I can recommend in addition to Christian's recommendation:
Paxton, P. M., Hipp, J. R., & Marquart-Pyatt, S. (2011). Nonrecursive models. Endogeneity, reciprocal relationships, and feedback loops. Thousand Oaks: Sage.
Frone, M. R., Russell, M., & Cooper, M. L. (1994). Relationship between job and family satisfaction: Causal or noncausal covariation? Journal of Management, 20(3), 565-579.
Wong, C.-S., & Law, K. S. (1999). Testing reciprocal relations by nonrecursive structural equation models using cross-sectional data. Organizational Research Methods, 2(1), 69-78.
Hi Holger, thank you for your answer and papers you recomended. I will read papers.
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