For specific models I would think that using the Mplus Model Constraint feature can accomplish that. You would constrain the parameters to generate a zero probability for a specific cell in your frequency table.
We have two variables of interest (A1 and A2) that involve a structural zero; the two variables cannot both = 1. However, we wanted to test the hypothesis that A1 reduces the likelihood of B, but B in turn increases the likelihood of A2. To test this hypothesis, I first ran a saturated model that included two probit regressions: B on A1; A2 on A1 B;
The coefficient for A2 on A1 was not statistically significant (p=0.980). I expected that if I removed that link from the model, I would get a model with good fit and with the other two regression coefficients remaining close to the values and significance they had exhibited in the saturated model. However, when I removed the link between A1 and A2, the p-value for the chi-square test of fit was 0.0000. Why is that? Is it related to the fact that there is a structural zero in the cross-tabulation of A1 and A2? If so, is there some alternative modeling technique that I can use to test our hypothesis?