Measurement invariance
Message/Author
 JackeJR posted on Wednesday, April 27, 2016 - 8:11 pm
A common way to test measurement invariance is to test it across groups e.g. Ethnicity.

If however I would like to test for measurement invariance across a continuous variable like age, how do I do it besides breaking age into age ranges?
 Bengt O. Muthen posted on Friday, April 29, 2016 - 6:46 pm
You can use the CONSTRAINT= option to let a measurement parameter vary as a function of say age. See also UG ex 5.23.
 JackeJR posted on Tuesday, May 10, 2016 - 12:58 am
Thanks Dr Muthen. I am not so sure I get it. What should I put under the model constraint? And how is this different from a MIMIC model?

A simple example below.

VARIABLE:
CONSTRAINT = AGE

MODEL:
f1 BY y1-y4;
f2 BY y5-y8;
f3 BY y9-y12;

MODEL CONSTRAINT
 Bengt O. Muthen posted on Tuesday, May 10, 2016 - 6:51 pm
Give a label to the loading you want to vary with age, say "load". Then say

Model Constraint:
New(a b);
load = a + b*age;

This way the loading is a linear function of age.
 JackeJR posted on Wednesday, May 11, 2016 - 12:05 am
Thanks Dr Muthen. Just to clarify, I run

VARIABLE:
CONSTRAINT = AGE

MODEL:
f1 BY y1-y4;
f2 BY y5-y8;
f3 BY y9-y12;
f1-f3(load);

MODEL CONSTRAINT
New(a b);
load = a + b*AGE;

A significant "b" suggests that age predicts the factor loading? or should I be comparing the model with constraints with the one without constraints to see if adding the constraints improve model fit?
 Bengt O. Muthen posted on Wednesday, May 11, 2016 - 7:15 pm
Yes, a significant b says that age predicts the factor loading.
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