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Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus

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  • Aguilera, Ana M.
  • Escabias, Manuel
  • Valderrama, Mariano J.

Abstract

The relationship between time evolution of stress and flares in Systemic Lupus Erythematosus patients has recently been studied. Daily stress data can be considered as observations of a single variable for a subject, carried out repeatedly at different time points (functional data). In this study, we propose a functional logistic regression model with the aim of predicting the probability of lupus flare (binary response variable) from a functional predictor variable (stress level). This method differs from the classical approach, in which longitudinal data are considered as observations of different correlated variables. The estimation of this functional model may be inaccurate due to multicollinearity, and so a principal component based solution is proposed. In addition, a new interpretation is made of the parameter function of the model, which enables the relationship between the response and the predictor variables to be evaluated. Finally, the results provided by different logit approaches (functional and longitudinal) are compared, using a sample of Lupus patients.

Suggested Citation

  • Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2008. "Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 151-163, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:151-163
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    1. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    2. Kazakevičiūtė, Agne & Olivo, Malini, 2017. "Point separation in logistic regression on Hilbert space-valued variables," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 84-88.
    3. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    4. Manuel Escabias & Ana Aguilera & M. Aguilera-Morillo, 2014. "Functional PCA and Base-Line Logit Models," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 296-324, October.
    5. Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.
    6. 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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