Wavelet-based scalar-on-function finite mixture regression models

Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. The classical finite mixture regression model is extended to incorporate functional predictors by taking a wavelet-based approach in which both the functional predictors and the component-specific coefficient functions are represented in terms of an appropriate wavelet basis. By using the wavelet representation of the model, the coefficients corresponding to the functional covariates become the predictors. In this setting, there are typically many more predictors than observations. Hence a lasso-type penalization is employed to simultaneously perform feature selection and estimation. Specification of the model is discussed and a fitting algorithm is provided. The wavelet-based approach is evaluated on synthetic data as well as applied to a real data set from a study of the relationship between cognitive ability and diffusion tensor imaging measures in subjects with multiple sclerosis.