In IRT models the difficulty of items has the same metric and equivalence to the ability of the people (both are in logits) I want to do the same with a CFA model. I want to have items in the same metric and equivalence as the factor scores of my only latent variable. How can I do this? I am using lavaan package in R and I have all the matrices (mean of items, variance covariance matrix and residual matrix of items) but I am stuck in that step. I have used a WLSMV algorithm because my data does not show a multivariate normal distribution.
Can somebody help me please? Thank you!
In CFA you have to anchor the metric of the latent variable, since it is in principle undeterminated. Two methods:
(1) set the variance of the factor to a value, usually 1
(2) set the loading of one item to 1, which means that the latent variable gets the same metric as this item.
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Dear Jan,
Thank you for your answer. I used method 2 to calculate my model. I got my standardized betas and unstandardized betas. Now I want to have those items values in the same metric of the factor scores. I need these in order to use the items to make cutting points and have the factor scores on one hand and groups of persons in the other.
Thank you!
Juan carlos! Hello! Mira si usaste el metodo dos, entonces tus factor loadings ya estan en la misma metrica que las variables latentes. solo tienes que poner la opcione de save factor scores (con o sin errores estandar) y grabarlos en un documento aparte. Luego puedes hacer merge con tu base de datos original y esos factor scores estaran ya en la misma metrica original de los items que incluiste en el modelo.
Karen!! Genial! Gracias! Me moveré entonces a Mplus porque eso en R es medio pesado. Muchas gracias!
Pd: Te tengo que escribir, tenemos un artículo ahí atorado que si tenemos que sacarlo para adelante...
¡Un abrazo y que estés re bien!
Hi Karen and Juan.
I am sorry my Spanish is not what it should have been (since I have never learned it). If you could make a resume in English, I would find it interesting.
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hi juan carlos and jan! sorry for the Spanish I just said the same as you and: if you used method 2, then your latent variables are already on the same metric as your raw items. what i do on mplus is just use this method (2) and then save latent scores per case on a different file (with the save latent score syntax). those latent scores would already be on the same metric and can be merged into your data set. should be similar for R. ps. yes JC lets get that paper published ;)
What I sometimes wonders, is what metric results if I link the factor to another item (I usually use method 1, so this have not been much of a concern to me). I tried once to investigate this, but I don't remember the result. I will try again.
I just tried, and
(1) the Factor scores are perfectly correlated whatever anchoring is used (var(FS)=1 ot loading(item1)=1 or loading(item2)=1 etc), but
(2) the metrics are different. Both means and variances are different.
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