Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus
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Ana M. Aguilera, Manuel Escabias, Mariano J. Valderrama, Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus, Computational Statistics & Data Analysis, Volume 53, Issue 1, 2008, Pages 151-163, ISSN 0167-9473, https://doi.org/10.1016/j.csda.2008.07.001
SponsorshipProject P06-FQM-01470 from ’’Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, Spain’’; Project MTM2007-63793 from Dirección General de Investigación, Ministerio de Educación y Ciencia, Spain
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.