Penalized logistic regression for functional data in the presence of latent class.
Marie Morvan

In this study, we propose a mixture of regression model suitable for the
prediction of a binary variable with functional covariates. Parameters of the model include
the covariance matrices of the covariables and coefficients of the regression model. They
are estimated using an EM algorithm. In the presence of a high number of covariates,
estimation of the full covariance matrix and interpretation of the regression coefficients is
intractable. To highligh relevant areas of the curve for the prediction and their links, we
apply a penalization to the covariance matrix and the regression coefficients. Automatic
selection tools are usedto choose the regularization constant associated to the best model
(among a finite set of models) according to the AIC criterion. The model’s performance
are evaluated with a simulation study, and an application on a set of spectrometric curves
used for the diagnostic of a chronic liver disease is presented.