Modeling variation in functional responses with applications in human motion analysis.

Abstract

This thesis develops a method to model the variability in functional data and illustrates it through applications to human motion data. We describe the methodology for modeling variation in functional responses through applications to human motion data. We begin with how to align the data curves appropriately, followed by a description of how to fit the data with models of various random effects structures, and then we illustrate how to display the results graphically. In addition to estimating the model parameters using R, we also used Win-BUGS, which is a program that implements the Markov Chain Monte Carlo method (MCMC). Furthermore, we compare the performances of the softwares by estimating parameters based on some simulated data. We consider how to model the simultaneous variation of two sets of functions to account for the correlation between different sets of functions. A method for partitioning the data curves into groups is then introduced which could make certain characteristics of the data curves more apparent when performing further analyses. We apply functional principal components analysis to investigate the sources of variability in the human motion data, and in addition, principal component scores are utilized to explore the effects of some predictors on variability. The simultaneous variation of two sets of functions is also examined by using functional canonical correlation analysis. Lastly, we illustrate how to construct and display a confidence region for the movement trajectory of a joint center in 3 dimensions.