Isotone additive latent variable models |
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Authors: | Sylvain Sardy and Maria-Pia Victoria-Feser |
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Institution: | (1) ENITIAA-INRA, Unit? de Sensometrie et Chimiometrie, Rue de la G?raudi?re, BP 82225, 44322 Nantes Cedex, France |
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Abstract: | For manifest variables with additive noise and for a given number of latent variables with an assumed distribution, we propose
to nonparametrically estimate the association between latent and manifest variables. Our estimation is a two step procedure:
first it employs standard factor analysis to estimate the latent variables as theoretical quantiles of the assumed distribution;
second, it employs the additive models’ backfitting procedure to estimate the monotone nonlinear associations between latent
and manifest variables. The estimated fit may suggest a different latent distribution or point to nonlinear associations.
We show on simulated data how, based on mean squared errors, the nonparametric estimation improves on factor analysis. We
then employ the new estimator on real data to illustrate its use for exploratory data analysis. |
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Keywords: | |
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