Factor loadings of indicators on a group factor switches when applied a bi-factor model

[Monica]

Hello.  I am trying to apply bi-factor model to a 3 factor model (each factor has 4 indicators).

When I apply a bi-factor model, two of indicators on a single factor show negative factor loadings, although they were originally positive.  I am wondering if it is acceptable to constrain factor loadings of these indicators to positive (e.g., 0.1)?

My bi-factor model is:

library(lavaan)

ABC.model <- 'A =~ NA*A1 + A2 + A3 + A4

B =~ NA*B1 + B2 + B3 + B4

C =~ NA*C1 + C2 + C3 + C4

G =~ NA*A1 + A2 + A3 + A4 + B1 + B2 + B3 + B4 + C1 + C2 + C3 + C4'

 fit <- cfa(ABC.model, data=Data, estimator="WLSMV", orthogonal=TRUE, std.lv=TRUE)

Thank you very much for your help!

[Terrence Jorgensen]

When I apply a bi-factor model, two of indicators on a single factor show negative factor loadings, although they were originally positive.  I am wondering if it is acceptable to constrain factor loadings of these indicators to positive (e.g., 0.1)?

Yes, that will yield an equivalent solution (all positive vs. all negative loadings yield the same model-implied Sigma).  You should only have to constrain one loading (per factor) to be positive in order for the rest to be positive in the solution.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Terrence Jorgensen]

When I apply a bi-factor model, two of indicators on a single factor show negative factor loadings, although they were originally positive.  I am wondering if it is acceptable to constrain factor loadings of these indicators to positive (e.g., 0.1)?

Yes, that will yield an equivalent solution (all positive vs. all negative loadings yield the same model-implied Sigma).  You should only have to constrain one loading (per factor) to be positive in order for the rest to be positive in the solution.

Woops, I didn't notice Jeremy's response, which somehow became a separate thread.  I noticed from his response that I missed the detail that it was not all loadings for that factor that were negative.  So my earlier response does not apply to your case.

[Monica]

I am sorry for the late response.  Thank you very much for your help!