2016-Statistical Theory and Modeling for Functional Data Analysis
Statistical Theory and Modeling for Functional Data Analysis
Organizer and Chair: Haocheng Li (University of Calgary)
[PDF]
Organizer and Chair: Haocheng Li (University of Calgary)
[PDF]
- KEXIN JI, University of Waterloo
Semiparametric Stochastic Mixed Models for Bivariate Periodic Longitudinal Data [PDF]
- We propose and consider inference for a semiparametric stochastic mixed model for bivariate periodic repeated measures data. The bivariate model uses parametric fixed effects for modelling covariate effects and periodic smooth nonparametric functions for each of the two underlying time effects. In addition, the between-subject and within-subject correlations are modelled using separate but correlated random effects and a bivariate Gaussian random field, respectively. We derive maximum penalized likelihood estimators for both the fixed effects regression coefficients and the nonparametric functions. The smoothing parameters and all variance components are estimated simultaneously using restricted maximum likelihood. We investigate the proposed methodology through simulation. We also illustrate the model by analyzing bivariate longitudinal female hormone data collected daily over multiple consecutive menstrual cycles.
- BEI JIANG, University of Alberta
Latent Class Modeling Using Matrix-valued Covariates with Application to Identifying Early Placebo Responders Based on EEG Signals [PDF]
- In this talk, we extend existing latent class models to incorporate matrix covariates. The proposed method is built upon a low rank Candecomp/Parafac (CP) decomposition to express the target coefficient matrix through low-dimensional latent variables, which effectively reduces the model dimensionality, and utilizes a Bayesian hierarchical modeling approach to estimating these latent variables, which provides a way to incorporate prior knowledge on the patterns of covariate effect heterogeneity and provides a data-driven method of regularization. Our simulation studies suggest that our proposed method is robust against potentially misspecified rank in the CP decomposition. We show that the proposed method allows us to extract useful information from baseline EEG measurements that explains the likelihood of belonging to the early responder subgroup.
- ZHENHUA LIN, University of Toronto
Mixture Models and Densities for Functional Data [PDF]
- We propose a novel perspective to represent infinite-dimensional functional data as mixtures, where the number of basis functions that constitutes the mixture may be arbitrarily large, but the number of included mixture components is finite and specifically adapted for each random trajectory. Within this framework, we show that a probability density can be well defined without the need for finite truncation or approximation. Dimensions of individual trajectories are treated as latent random variables and a modified expectation-maximization algorithm is adopted for model fitting. Simulations confirm that comparing to traditional FPCA the proposed method achieves similar or better data recovery while using fewer components on average. The practical merits of functional mixture modeling are demonstrated by analyzing egg-laying trajectories for medflies.