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Mplus Discussion > Confirmatory Factor Analysis >
 Christopher Cerasoli posted on Wednesday, September 29, 2010 - 11:31 am

When conducting CFA's, you have to impose model constraints to give your latent variables a scale. Often, we fix one of the factor loadings of an observed variable onto a latent variable to 1.00. I realize that the factor loading to fix (usually to 1.00) is arbitary as far as overall model fit is concerned. However, this choice has a substantial impact on individual model parameters.

Can you suggest whether (or how) it is appropriate to choose which factor loading should be fixed?

Thank you!
 Linda K. Muthen posted on Thursday, September 30, 2010 - 12:16 pm
In response to your statement that the choice of the loading fixed to one has a substantial impact on models parameters, note that all standardized solutions will be the same. These are just alternative parametrizations that give the same model fit.

Usually one chooses the largest factor loading.
 Christopher Cerasoli posted on Tuesday, December 07, 2010 - 6:50 am

Thank you for your reply. I've also found that Ken Bollen's (1989) book recommends scaling the factor loading/coefficient to one by convention as you suggest(pp. 91, 239).

Can you recommend a method for choosing the factor with the largest loading and if possible provide a citation? The only thing that comes to mind is either EFA or trial and error.

As an aside, a colleague recently provided me with a paper by Little, Slegers, & Card (2006), suggesting several scaling methods that can make the metric of the latent variables more readily interpretable.

Thank you,

 Linda K. Muthen posted on Tuesday, December 07, 2010 - 8:01 am
To see all factor loadings, free the first factor loading and fix the factor variance to one.
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