# Interpretation / use of "slack" values

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### TBP

Jun 1, 2019, 2:37:45 PM6/1/19
to lavaan
Fixing coefficients as variables in Lavaan provides a "slack" value output. I have hunted around and I don't see any guidelines for interpreting this. If it is referenced at all, it is usually a single sentence saying it can be used to evaluate the validity of a constraint and 0.00 is good. Since I don't see any discussion of it on this group yet and this group is the repository for all things lavaan, can someone explain what that value is and if there are any rules of thumb for its interpretation?

A few specific questions (but I am interested in whatever people want to say about slack):
-If we have a priori data/hypotheses that suggest path relationships should be 0 or + or - could I use a>0 or a<0 or a==0 as an explicit test of this? How would that be specified?
If we belie
Z=~a*W+b*X+c*Y
a==0  - if we believe that this path should not have an influence for a given set of data
b<0  - if we believe b should have a negative influence?
c>0   - if we believe c should have a positive influence?

-If so, how do I interpret that slack value?

### Terrence Jorgensen

Jun 3, 2019, 5:57:58 PM6/3/19
to lavaan
it can be used to evaluate the validity of a constraint

This is not about testing a null hypothesis.  The slack should be nearly zero, indicating that the optimizer found a solution that matches your constraint.  The larger the slack, the further away the solution is from your intended constraint.

If we have a priori data/hypotheses that suggest path relationships should be 0 or + or - could I use a>0 or a<0 or a==0 as an explicit test of this?

You want to test a null hypothesis, so do not put the constraint in your syntax.  Just fit the unconstrained model 'Z=~a*W+b*X+c*Y', then use lavTestWald() to test the constraint that 'a == 0'.

lavaan does not directly provide tests of inequality (> or <) constraints, but if you are really just fitting linear regression models, you can use the restriktor package for that.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam