Model Constraint details
Message/Author
 Scott Morris posted on Thursday, June 28, 2018 - 8:56 am
I am trying to figure out if I can use the Model Constraint function to compute a function of item parameters in an ordinal CFA model.

I have two questions:
1) Where can I find details on the operations and functions permitted in the Model Constraint command (e.g., is there a way to compute item response probabilities from a probit model)?
2) When I create a new variable using a loop, I get an estimate as a single value in the output. How is this estimate computed?

Specifically I want to to compute NCDIF, i.e.,
SUM (wi(F1 - F2)^2)/(SUM(wi),
where F1 and F2 are logit or probit functions of the item parameters and the latent variable, and wi is the density function of the latent variable.

Thank you.
 Bengt O. Muthen posted on Thursday, June 28, 2018 - 2:39 pm
1) See the V8 UG pages 641-642 - all these are available also for Model Constraint, including the PHI function for probit.

2) If for instance you are using ML, the new function of the ML estimates for the parameters used in the function is in itself an ML estimate. It gets a SE and a CI. The SUM function is not available in Model Constraint.
 Scott Morris posted on Thursday, June 28, 2018 - 8:19 pm
Thanks. This is very helpful.

But I'm still confused about how estimates of functions are obtained when the function involves a loop.

Say I have,

Model Constraint:
NEW (p1);
LOOP (f, -3, 3, 0.1);
p1 = 1/(1 + EXP(tau1 - lambda1 * f));

where tau1 and lambda1 are parameters.

When I run this I get a single estimate and SE for p1 in the output. But since p1 is a function of the loop variable f, how does it result in a single value in the output?
 Bengt O. Muthen posted on Saturday, June 30, 2018 - 2:44 pm
I think you want to use LOOP option together with PLOT(p1) instead of having p1 in the NEW option. Then you get a confidence interval for each f value.