Ordered model constraint of item prob...
Message/Author
 Juergen Schneider posted on Tuesday, August 11, 2015 - 2:53 am
Dear MPlus enthusiasts,
I am computing a LCA with 5 dichotomous indicators and 4 classes. My theoretical assumptions make me want to constrain the item probabilities in an ordered fashion. Example for item 1: Probability of item 1 should be lowest in class 1, higher in class 2, higher in class 3 and highest in class 4.
In mathematical expression: p(11) < p(12) < p(13) < p(14)
I realized these model constraints for all items in the "model constraints" section of MODEL. The output however gives me
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE
COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.
-> Is it possible to constain the parameters in an ordered fashion?
-> Is it possible to do this like I did it (see below) or is there any other possibility?
------------
MODEL:
%class#1%
[item1\$1] (it11);
[item2\$1] (it21);
[item3\$1] (it31);
[item4\$1] (it41);
[item5\$1] (it51);
%class#2%
[item1\$1] (it12);
[item2\$1] (it22);
[item3\$1] (it32);
[item4\$1] (it42);
[item5\$1] (it52); !..and so on, defined for all classes
MODEL CONSTRAINT:
it11 < it12; !constraints item 1
it12 < it13;
it13 < it14; !..and so on, defined for all items
 Bengt O. Muthen posted on Tuesday, August 11, 2015 - 1:49 pm
Your approach seems ok, but you can also use Model Constraint to ensure the ordering by a re-parameterization like

p12 = p11+exp(c1);
p13 = p11+p12 +exp(c2);

etc

where the exponentiation makes for a non-negative increment.