Vivo Gharib posted on Monday, February 01, 2016 - 7:23 am
Dear Dr. Muthen A]My research: A System of 3 Simultaneous Eq's with 3 endog responses which r binary & ordinal & r observed. I am hypothesizing a simultaneous relationship between them. Cross-sectional study. Sample size 500. Suppose the system is identified.
B]My Objective: to model my sys. by at least 2 modeling techniques & choose the best, referring to the theoretical framework. I am very new with this topic. I need to confirm correctness of some deduced points: 1)Simultaneous Eq's in case of categ responses can be modeled by: a) Traditional regression methods using the approach of the Generalized Linear Modeling b) Regression methods using the approach of Latent Response Formulation c) Path Analysis d) SEM 2)In (a&b) no mediation nor latent construct analysis 3)Estimation methods for (a) & for (b) r the same e.g. 2-stage IV, 3-stage IV, LIML, FIML,
C]My questions for you: 1)If I don't do mediation analysis in (c&d) nor latent construct analysis in (d), will the 4 techniques give similar results about: the estimators' significance, the estimators' values & the MSE? & then the comparison doesn't make sense. 2)In contrast, if I do the mentioned analyses, & in (a&b) the latent constructs r created by traditional factor analysis, will the 4 tech.'s give different results? Best Regards
If you just have 3 equations with no cross-equation restrictions or any path analysis going on, I think your ML (or Bayes) solution when analyzing all 3 together in one run will be the same as doing the 3 separately.
I don't know how the 4 estimators compare.
Vivo Gharib posted on Tuesday, February 02, 2016 - 6:32 pm
Dear Dr. Muthen I think my message wasn't clear enough. Suppose my system of the 3 simultaneous equations is: Y1 = f1 (Y2, Y3, X1) Y2 = f2 (Y1, Y3, X2) Y3 = f3 (Y2, X3) Y1 & Y2 are ordinal, Y3 is binary X1 , X2 , and X3 are vectors of indep. variables. They contain similar and different x's of each others.
I plan to model the system using each of the 4 techniques of modeling (mentioned in my past message), then choose the best among them (the one that match the theoretical framework of my variables). N.B.: I mean by methods (a & b) the traditional modeling methods of the response processes in the simultaneous eq. context, where 2 or 3 stage instrumental var's estimation technniques are used.
My question: is it known already in the literature that these 4 techniques of modeling give similar (or different) results (estimators' significance, estimators' values & the MSE)?
Waiting for the help.
Vivo Gharib posted on Tuesday, February 02, 2016 - 6:54 pm
sorry, Dr. Muthen, when you read my second message please read this clarification too:
* I mean by method (c) that i'll allow for a mediation analysis in it.
* I mean by method (d) that i will allow for a mediation analysis and a latent constructs (factors) analysis in it.
* In methods (a) & (b), i will create the latent constructs by the traditional factor analysis & then i'll embed them in the simultaneous equations as explanatory variables. Then no mediation analysis nor latent constructs (factors) analysis are allowed in methods (a & b).
* The famous estimation methods that maybe i'll try with (a & b) are 2-stage IV, 3-stage IV, & also Limited Inforamation Maximum Likelihood (LIML), and Full Information Maximum Likelihood (FIML). While for techniques (c & d), i'll try the Covariance-based estimation methods (i haven't studied yet) and maybe the Construct-based estimation methods e.g. the Partial Least Squares (PLS).
Waiting for the help.
Vivo Gharib posted on Wednesday, February 03, 2016 - 6:06 pm
Dear Dr. Bengt O. Muthen, Dr. Linda K. Muthen, and anybody who may help,
I need any help, advice, or comments on my research problem, please. Please have a look on my past 3 messages.
I don't know the answers to these research questions. Perhaps you can ask on SEMNET.
Vivo Gharib posted on Friday, February 05, 2016 - 12:08 am
Thank you very much for the reply.
Vivo Gharib posted on Wednesday, February 10, 2016 - 3:29 pm
Dear Dr. Bengt,
You have kindly guided me to the SEMNET forum. Then, I have seen there an old message (from the year 2005), stating that the following model (#1) can't be handled by any SEM software even Mplus. The stated reasons are: the model is non-recursive, having more than 2 responses, and the responses are non-continuous.
My question: is it still impossible to handle Model #1 using later editions of Mplus. And, what about Models #2 & #3, can Mplus handle them?
Model #1 Y1 = f1 (Y2, Y3, X1) Y2 = f2 (Y3, X2) Y3 = f3 (Y2, X3)
Where, Y1 & Y2 are ordered categorical (ordinal) variables, and Y3 is binary (dichotomous) variable
X1 , X2 , and X3 are vectors of independent (continuous & non-continuous) variables. They contain similar and different x's of each others. f1, f2, f3 are the suitable functions.
Cross-Sectional analysis, Sample size 500. Suppose the model specification has passed the identification test.
Model #2 (recursive) Y1 = f1 (Y2, Y3, X1) Y2 = f2 (X2) Y3 = f3 (Y2, X3) With same definitions as in Model #1
Model #3 Y1 = f1 (Y2, Y3, X1) Y2 = f2 (Y1, Y3, X2) Y3 = f3 (Y1, Y2, X3) With same definitions as in Model #1