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Repeated measures in functional logistic regression

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  • Urbano-Leon, Cristhian Leonardo
  • Aguilera, Ana María
  • Escabias, Manuel

Abstract

We present a proposal to extend the functional logistic regression model – which models a binary scalar response variable from a functional predictor – to the case where the functional observations are not independent because the same functional variable is measured in the same individuals in different experimental conditions (repeated measures). The extension is addressed by including a random effect in the model. The functional approach of this model assumes that all functional objects are elements of the same finite-dimensional subspace of the space of square-integrable functions L2 in the same compact domain allowing the functions to be treated through the basis coefficients on the basis that spans the subspace to which functional objects belong (basis expansion). This methodology usually induces a multicollinearity problem in the multivariate model that emerges, which is solved with the use of the functional principal components of the functional predictor, resulting in a new functional principal component random effects model. The proposal is contextualized through a simulation study that contains three simulation scenarios for four different functional parameters and considering the lack of independence.

Suggested Citation

  • Urbano-Leon, Cristhian Leonardo & Aguilera, Ana María & Escabias, Manuel, 2024. "Repeated measures in functional logistic regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 66-77.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:66-77
    DOI: 10.1016/j.matcom.2024.05.002
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    References listed on IDEAS

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    1. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    2. Łukasz Smaga, 2020. "A note on repeated measures analysis for functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 117-139, March.
    3. Christian Acal & Ana M. Aguilera, 2023. "Basis expansion approaches for functional analysis of variance with repeated measures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 291-321, June.
    4. Cristhian Leonardo Urbano-Leon & Manuel Escabias & Diana Paola Ovalle-Muñoz & Javier Olaya-Ochoa, 2023. "Scalar Variance and Scalar Correlation for Functional Data," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    5. Ana M. Aguilera & Manuel Escabias & Francisco A. Ocaña & Mariano J. Valderrama, 2015. "Functional Wavelet-Based Modelling of Dependence Between Lupus and Stress," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 1015-1028, December.
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