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.
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".
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.
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.
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?