CONTENTS OF THIS FOLDER ——————————————

• MD_FPCA_Tutorial.m : Step-by-step implementation of MD-FPCA algorithm using the MultilevelFuncLong.m function. MultilevelFuncLong.m assumes data is densely observed on a regular grid in the functional domain and observed either with or without sparsity on a regular grid in the longitudinal domain.

• multilevel_func_data.mat : Sample dataset for performing MD_FPCA_Tutorial.m

• Multilevelfunctong.m : Fits a MD-FPCA model to repeated multilevel functional data. MultilevelFuncLong.m assumes data is densely observed on a regular grid
  in the functional domain and observed either with or without sparsity on
  a regular grid in the longitudinal domain. Please refer to the MD-FPCA algorithm in Web Appendix A for annotation of MultilievelFuncLong.m steps.

• MultilevelFPCA.m : Fits a multilevel FPCA model to multilevel functional data.

• MeanSmooth2D.m : Performs local weighted least squares kernel smoothing on a two-dimensional with user specified bandwidths or a bandwidth selected from a list of candidates by GCV.

• mean2dKH.m : Performs local weighted least squares kernel smoothing on a two-dimensional with user specified bandwidths.

• getRawCovKH.m : Finds the total raw covariance and the level one raw covariance for multilevel FPCA implementation.

• gcv_mullwlsn_MFPCA.m : Performs covariance smoothing and bandwidth candidate selection.

• CovarianceSmooth.m : Performs covariance smoothing with bandwidth candidate selection or user specified bandwidths.

• ComputeScores.m : Computes scores for multilevel data using BLUP of Di et al. (2014).

INTRODUCTION ——————————————

The contents of this folder allow for implementation of the MD-FPCA decomposition described in "A multi-dimensional functional principal components analysis of EEG data " by Hasenstab and Scheffler et al. (2017) (http://onlinelibrary.wiley.com/doi/10.1111/biom.12635/epdf). Users may apply the proposed MD-FPCA decomposition (Multilevelfunctong.m) to the sample dataset multilevel_func_data.mat. Detailed instructions on how to perform the aforementioned procedure and visualize results are included in MD_FPCA_Tutorial.m. The remaining functions are dependencies that are called by Multilevelfunctong.m.

REQUIREMENTS ——————————————

The included Matlab programs were developed using Matlab 2015b and require the Matlab package PACE v. 2.17 (http://www.stat.ucdavis.edu/PACE/).

INSTALLATION ——————————————

Place Matlab .m files and PACE v. 2.17 (http://www.stat.ucdavis.edu/PACE/) into working directory, along with the multilevel_func_data.mat file. These will be used to implement and demonstrate the MD-FPCA algorithm through steps detailed in MD_FPCA_Tutorial.m.