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Functional PCA and Base-Line Logit Models

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Abstract

In many statistical applications data are curves measured as functions of a continuous parameter as time. Despite of their functional nature and due to discrete-time observation, these type of data are usually analyzed with multivariate statistical methods that do not take into account the high correlation between observations of a single curve at nearby time points. Functional data analysis methodologies have been developed to solve these type of problems. In order to predict the class membership (multi-category response variable) associated to an observed curve (functional data), a functional generalized logit model is proposed. Base-line category logit formulations will be considered and their estimation based on basis expansions of the sample curves of the functional predictor and parameters. Functional principal component analysis will be used to get an accurate estimation of the functional parameters and to classify sample curves in the categories of the response variable. The good performance of the proposed methodology will be studied by developing an experimental study with simulated and real data.

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Author information

Authors and Affiliations

  1. Facultad de Farmacia, Universidad de Granada, Campus de Cartuja, 18071, Granada, Spain

    Manuel Escabias

  2. Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva, 18071, Granada, Spain

    Ana M. Aguilera

  3. Departamento de Estadística, Universidad Carlos III de Madrid, Avda. de la Universidad, 30., 28911, Leganés, Spain

    M. Carmen Aguilera-Morillo

Authors
  1. Manuel Escabias
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  2. Ana M. Aguilera
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  3. M. Carmen Aguilera-Morillo
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Corresponding author

Correspondence to Manuel Escabias.

Additional information

This research was supported by Projects MTM2010-20502 from Dirección General de Investigación del MEC, Spain, and FQM-08068 from Consejería de Innovación, Ciencia y Empresa de la Junta de Andalucía Spain. We want to thank the referees advisers.

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Escabias, M., Aguilera, A.M. & Aguilera-Morillo, M.C. Functional PCA and Base-Line Logit Models. J Classif 31, 296–324 (2014). https://doi.org/10.1007/s00357-014-9162-y

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  • DOI: https://doi.org/10.1007/s00357-014-9162-y

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