predicting more than one factor with FA

[Marco d'Errico]

Dear Stata users.

a quick question for all of you.

I run a FA and got results that include more than one factor. But then, when getting to the prediction part, you can predict as many factors as you want (well in fact as many as there are) but you cannot predict ONE single variable which includes a decided # of factors.

Actually I would like to predict a variable which include as many factors as needed in order to detect at least 90% of the variance of the observed variables.

Is there any way stata can do this?

[daniel klein]

This appears to be a misunderstanding. One variable cannot represent more than (the scores of) one factor. If e.g. your first two factors account for at least 90 % of the variance, you merely predict two new variables containing the factor scores of the first two factors. If you need three factors to account for the same amount of variance, you predict three variables and so on.

Best
Daniel

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[Nick Cox]

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Your request makes no sense to me.

If it were possible to have a single constructed variable that "detected" at least 90% of your total variance, then it would already be your first factor. You can't do better than the first factor in explaining fraction of variance; that's either a definition or a consequence of what factor analysis does, subject to small print defining the particular factor analysis solution identified.

What you can do is use several factors together in some subsequent regression-like modelling, and this may be what you are after. Using several factors in later regression doesn't seem as fashionable as it once was, but it is perfectly possible. Many researchers would rather use the original variables as predictors.

For "factors" read also "principal components" as appropriate.

[Marco d'Errico]

Dear both thank you for the responses. I have just sent an email to administration asking to change my name. I didn't know!

I try to specify my question a bit better.
let's assume that factor 1 explains say 70%; f2 explains 15%; f3 explains 10% and finally the other factors explain the rest.

F1 explains something, most likely explains better some variables and less of others; and so do f2 and f3.
If I want to use the whole bunch of information, i.e.: putting together the three factors that explain the 70+15+10=95% of the variance, how can I do?

it's like when in psychometrics you try to explain intelligence; you use some proxies and f1 can be explaining handling capacity; f2 logic and f3 something else. but then you want to combine/aggregate this information and measure intelligence.
how is it doable? or.. maybe better: is it doable?

thank you again!
Marco

[daniel klein]

This is getting kind of interesting. I guess basically you should think about the structure of your models here. Factor analysis assumes one or more latent variables (dimensions) that affect a bunch of manifest indicators. This is called a reflective model and is different from a formative model, in which more than one manifest indicator constitutes a latent construct. I would think in the direction of SEM and/or sheaf-coefficients, I guess. As you can tell, I am all but an expert on this - but interested anyway.

Best
Daniel

[ben earnhart]

Nick had it exactly right for an EFA with no constraints -- if it were possible to have a factor that explained 95% of the variance, then it already would be F1 The best you can do is to force the number of factors down with the factors() option, say reduce it to two factors or even force a single factor. See how much of the variance is explained. If you get 95%, then you're set (at the cost of having something less substantively interpretable). This would go for an EFA or a SEM approach. Also, note that the overall variance explained will go down as you reduce the number of factors, so the chances of getting to 95% explained are much less than by having multiple factors.

That's a problem with uni-dimensional intelligence scales -- by forcing all the variance into a single construct, we lose the ability to really say what it's measuring other than variance explained in the items in the scale. If you let your EFA or SEM have several dimensions, then ideally, the different dimensions have substantively interpretable meanings.

So if it's independent variables in a model, you'd probably be better off with multiple factors. It complicates your interpretation in some ways since you have different effects for different factors, but it should improve fit and give a more *meaningful* interpretation. If it's a dependent variable you're trying to construct, then a SEM approach will let you model the several factors simultaneously.