Re: Fixing latent factor correlation -not covariance- to 1

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Terrence Jorgensen

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Dec 9, 2018, 1:14:15 PM12/9/18
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I am new to lavaan after AMOS and I was wondering how I can fix the correlation between two latent factors to 1.

Cor(X,Y) $= 1 = \frac{\text{Cov(X,Y)}}{\text{SD(X)} \times \text{SD(Y)}}$, so Cov(X,Y) $= \text{Cor(X,Y)} \times \text{SD(X)} \times \text{SD(Y)}$

So you can fix a covariance to the equivalent of a correlation = 1 by labeling the factor (co)variance estimates and using them to define a constraint.

X =~ ...
Y
=~ ...
X
~~ psi11*X + psi21*Y
Y
~~ psi22*Y
## model constraint
psi21
== sqrt(psi11 * psi22)


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

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