Abstract
We consider Factor Analysis models representing two blocks of variables and discuss the problem of "identifiability" or what we rather prefer to name model selection. For general Factor Analysis (or equivalently, for Error in Variables) models this problem is apparently still unsolved although raised and discussed in the literature since more than fifty years ago.
In this paper we show that there is a continuum of representations which connect together two extreme representations of the pure regression type. This continuum of models can be parametrized in terms of a projection matrix describing the part of the modelled vector which is represented exactly (i.e. with no random modelling error) by the Factor Analysis model. Any procedure of model selection is just a procedure for choosing the "exact part" of the modelled variables. Any choice results in certain modelling errors for the remaining variables, whose variance can be computed explicitly.
On leave from Istituto di Elettrotecnica ed Elettronica, Università di Padova, 35100 PADOVA, Italy
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© 1988 Springer-Verlag
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Picci, G. (1988). On the identifiability of factor analysis models. In: Byrnes, C.I., Kurzhanski, A.B. (eds) Modelling and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043192
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DOI: https://doi.org/10.1007/BFb0043192
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