# Equal threshold intervals in SEM with categorical variables

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### tran viet Yen

Feb 21, 2019, 3:09:05 AM2/21/19
to lavaan
Dear all,

When estimating a SEM with categorical variables using, can we constrain the intervals between thresholds? For instance in this simple model with the latent variable A and two indicator A1 and A2:

A =~ A1 + A2
A1 | a1*t1 + a2*t2 + a3*t3 + a4*t4
A2 | a1*t1 + a2*t2 + a3*t3 + a4*t4

The problem is, if I want to place some constraints on the thresholds, for instance to force a2 = -a3 and (a2-a1) = (a4-a3) like in this picture:

then how we will modify the code to obtain this?

Thank you so much for reading this topic.

Best,

Tran Viet Yen.

### Terrence Jorgensen

Feb 21, 2019, 4:04:10 PM2/21/19
to lavaan
how we will modify the code to obtain this?

You can literally put those in your model syntax, using the "==" operator to define any (in)equality constraint(s) on labeled parameters.  But you need to express the left-hand side as a single parameter, which can be user-defined.

`model <- '`
`A =~ A1 + A2A1 | a1*t1 + a2*t2 + a3*t3 + a4*t4A2 | a1*t1 + a2*t2 + a3*t3 + a4*t4`
`a2 == -1*a3 diff21 := a2 - a1diff43 := a4 - a3diff21 == diff43'`

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

### tran viet Yen

Feb 22, 2019, 1:25:05 AM2/22/19
Dear Terrece,

Thank you very much for the instructions. This is exactly what I'm looking for. You have explained it in a very detailed manner.

Best regards,

Tran Viet Yen.

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