Is it necessary to fix covariance to zero when the variance of a factor is fixed at zero?

Question

When I conducted sem using lavaan, I found the variance of a factor was negative. So I fixed the variance of this factor to be zero. Should I fix the covariance with this factor also to be zero? I knew that in Mplus, when one constrained the variance to be zero, its covariance would automatically be zero. Is it necessary to set the covariance to zero?

Answer 1

Fixing negative variance estimates to 0 is not a good idea:

https://doi.org/10.1037/1082-989X.13.2.150

https://doi.org/10.1177/0049124112442138

https://doi.org/10.1037/met0000384

But indeed, lack of variance implies lack of covariance, so you would have to (in lavaan) make that factor orthogonal to be consistent.