Low factor loadings on latent variable in SEM

[jesse]

Dear TalkStats,

I am fitting a structural equation model and one of the latent variables has 3 out of 5 factor loadings under .60 I heard that this may be a cut off point for legitimate loadings, but I can't find a reference. In any case, both the measurement model and the structural model have high GFI scores, and the model is well grounded in theory. (Also, I am using standardized coefficients.)

Is the latent variable with low (<.6) factor loadings a cause for concern?

Jesse

 

[Lazar]

There is a common misconception that model fit in SEM has something to do with the size of the estimates (i.e. factor loadings). This is not the case. Rather fit is based on the parameters that are constrained either to zero or to a particular value (i.e. paths you could have estimated but didn't). Thus the fact your model fits well but has low loadings need not be surprising.

Having said that is < .6 factor loadings a problem (I am assuming here that the .60 loadings are standadized). Well it depends. It suggests the items in your measure are poor (my guess is that the reliability is low). It also suggests that any analysis using manifest scale scores is clearly inappropriate BUT the point of SEM is to control for this unreliability so if you are going to use the latent in regression or something then I would see how well the measure does in that job and make a judgement based on that.

P.S. I have seen this .60 rule of thumb before and like all rules of thumb it does not generalise well from the context in which it was developed.

 

[jesse]

Your answer is clear and very helpful. Thank you.

I have checked the internal reliability of the construct, and the Chronbach's alpha is .732. Based on your advice, I will go ahead with the analysis.

 

[jrai]

Standardized factor loadings in SEM when squared have same interpretation as R-square in regression. This is only valid when only 1 latent variable loads on an observed variable. If multiple latent variables load on the same measured variables then we cannot use this interpretation. Factor loading of 0.6 means that the latent variable explains 36% of the manifest variable, which I think isn't bad enough for discarding.