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

[Terrence Jorgensen]

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

http://www.uva.nl/profile/t.d.jorgensen