Non-recursive path model
Message/Author
 Hans Berten posted on Thursday, September 07, 2006 - 8:23 am
Dear dr. Muthén,

My question is the following: is it possible to handle a non-recursive path model in M-Plus with a categorical and a continuous endogenous variable (no latent variables)?
For example:

VARIABLE: USEVARIABLES ARE y1 y2 x1 x2 x3 x4 x5 x6;
CATEGORICAL IS y2;
MISSING ARE ALL (999);
ANALYZE : ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL: y1 ON y2 x1 x2 x3 x4 x5;
y2 ON y1 x1 x2 x3 x4 x6;

Is it possible to analyse this model using the ML estimator? It seems to work only when using WLSMV (and with theta parameterization). When I try to analyze this non-recursive model choosing ML estimator I get the fatal error message: reciprocal interaction problem.

Do I need to constrain the model by fixing the covariance between the residuals y1 and y2 to zero? If yes, how does it work?

The same problem arises when I try this model in a multilevel analysis.

 Bengt O. Muthen posted on Thursday, September 07, 2006 - 9:19 am
Here is a post from SEMNET some time ago -the last paragraph is relevant to your question.

I want to expand on Cameron McIntosh's answer to Ricardo on Friday
regarding a recursive model with one continuous and one dichotomous
DV. Cameron's said that categorical-variable SEM methods can handle the
situation if the observed dichotomous DV is (i) a "categorized version of a
continuous variable", but not when it is (ii) "truly categorical".

Consider Model A,

(1) y1 = beta_1 * y2* + gamma_1 * x1 + e1,
(2) y2* = gamma_2 * x2 + e2,

where y1 is a continuous observed variable and y2* is a continuous latent
response variable underlying the dichotomous observed variable y2. Here,
y2 =0/1 depends on y2* exceeding a threshold or not. This is the standard
categorical-variable SEM model, where the case (i) specification is made in
(1). The model where y1 influences y2* instead of being influenced by y2*
also falls into this standard case.

In contrast, Model B

(3) y1 = beta_1 * y2 + gamma_1 * x1 + e1,
(4) y2* = gamma_2 * x2 + e2,

lets the observed dichotomous y2 influence y1 as seen in (3) and therefore,
I think, represents the "truly categorical" case (ii). Note that in (4)
the y2* construction is not necessary because (4) is simply a standard
probit/logit regression model. In Mplus, Model A can be estimated via WLS
using probit and Model B can be estimated via ML using logit.

Similar modeling topics have been discussed in the 1983 article by Winship
& Mare. Note also that a corresponding non-recursive, i.e. reciprocal
interaction, version of Model B is internally inconsistent unless beta_1 or
beta_2 is zero - see Maddala's 1983 book, pp. 117-118 (Model 1), leading
back to the recursive case.

Bengt Muthen
 Becky McNeil posted on Monday, September 23, 2013 - 1:48 pm
Dear Drs. Muthen,

I have been working with a path model with a mixture of continuous, ordinal, and binary endogenous variables. The model uses the ML estimator and montecarlo integration. It was recently suggested that we evaluate the possibility of a bidirectional relationship between two of the variables. Adding the reverse direction to the existing model statements yielded a message of FATAL ERROR: RECIPROCAL INTERACTION PROBLEM.

Can bidirectional relationships be fit using ML and montecarlo? Are there any specific criteria that must be met?

Thank you for your time,
Becky
 Linda K. Muthen posted on Monday, September 23, 2013 - 2:23 pm
Please send the output and your license number to support@statmodel.com.
 Tom Bailey posted on Wednesday, April 09, 2014 - 6:16 pm
Dear Dr Muthen

I was hoping you may be so kind as to advise on an issue I am having when I run a bi-directional path in one of my models. I get much larger standardised path estimates for both variables in this relationship, and much bigger standard errors to boot. It also no longer calculates an interpretable r squared for either variable.

I have run the model (below) with a variety of estimators and the results are similar, if you could advise me on what I should or shouldn't be doing in this context I would be very grateful

Regards

Tom

MODEL: SRJP BY NPARCJ1 NPARCJ2 NPARCJ3 ;

ADV BY A1 A4 A5 ;
SELE BY F1 F4 F5 ;

SRJP ON ADV SELE;
ELE ON SRJP ;

ANALYSIS: ESTIMATOR = WLSMV ;

OUTPUT: standardized; modindices; TECH4 ;
 Linda K. Muthen posted on Thursday, April 10, 2014 - 9:47 am
Do you mean

SRJP ON ADV SELE;
SELE ON SRJP ;

I believe you must have a covariate in sele ON srjp that is unique like you have in the other regression.

You might want to see what Ken Bollen says in his SEM book.