>Steven Carchon wrote: >> >> During my statistical reading, I encountered the following : "the >> factor model is generally not identifiable". What does this mean >> actually and when is a factor model identifiable then ? What are the >> conditions ?
>In article <[EMAIL PROTECTED]>, >Bob Wheeler <[EMAIL PROTECTED]> wrote: > >It basically means that it is a figment of one's >imagination. Technically, a non-identifiable model is not >unique -- the data can be explained as well by other models. >It may be that the authors you cite, were thinking about the >fact that alternative "meaningful" patterns can be obtained >by rotating the factors; although there are more serious >identifiably problems. No, non-identifiability does not mean that model is "figment of one's imagination". Lot's of perfectly good models are non-identifiable. There is nothing wrong with such models. Non-identifiability is simply a technical problem in some situations (it seems to be especially annoying to people trying to prove theorems about consistency of maximum likelihood estimates). It causes real problems only if you wrongly thought that the non-identifiable aspects were meaningful. For example, a one-factor model will be non-identifiable because you can change the sign of all the parameters without changing the distribution of the observable variables. This corresponds to changing the sign of the latent factor. This is a trivial change of scale of no real significance. With more than one factor, the model is non-identifiable with respect to more general rotations of the latent factor space. This causes no problems as long as you realize that its the latent factor space, not any particular coordinate system for it, that you are finding. Regrettably, much work has gone into trying to identify the unidentifiable in this instance, but that's not the fault of the factor analysis model. Radford Neal . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
