Applied Functional Data Analysis: Methods and Case Studies
Almost as soon as we had completed our previous book Functional Data Analysis in 1997, it became clear that potential interest in the ?eld was far wider than the audience for the thematic presentation we had given there. At the same time, both of us rapidly became involved in relevant new research involving many colleagues in ?elds outside statistics. This book treats the ?eld in a di?erent way, by considering case st- ies arising from our own collaborative research to illustrate how functional data analysis ideas work out in practice in a diverse range of subject areas. These include criminology, economics, archaeology, rheumatology, psych- ogy, neurophysiology, auxology (the study of human growth), meteorology, biomechanics, and education—and also a study of a juggling statistician. Obviously such an approach will not cover the ?eld exhaustively, and in any case functional data analysis is not a hard-edged closed system of thought. Nevertheless we have tried to give a ?avor of the range of meth- ology we ourselves have considered. We hope that our personal experience, including the fun we had working on these projects, will inspire others to extend “functional” thinking to many other statistical contexts. Of course, manyofourcasestudiesrequireddevelopmentofexistingmethodology,and readersshouldgaintheabilitytoadaptmethodstotheirownproblemstoo.
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682 The growth data
Time Warping Handwriting and Weather Records
72 Formulating the registration problem
73 Registering the printing data
74 Registering the weather data
75 What have we seen?
762 Estimation of the warping function
How Do Bone Shapes Indicate Arthritis?
23 Functional principal component analyses
232 Smoothing the PCA
234 Detailed examination of the scores
24 What have we seen?
25 How are functions stored and processed?
252 Fitting basis coefficients to the observed data
253 Smoothing the sample mean function
254 Calculations for smoothed functional PC A
26 Crossvalidation for estimating the mean
27 Notes and bibliography
The Nondurable Goods Index
32 Transformation and smoothing
33 Phaseplane plots
34 The nondurable goods cycles
35 What have we seen?
36 Smoothing data for phaseplane plots
Bone Shapes from a Paleopathology Study
42 Data capture
43 How are the shapes parameterized?
44 A functional principal components analysis
45 Varimax rotation of the principal components
47 What have we seen?
Modeling ReactionTime Distributions
52 Nonparametric modeling of density functions
53 Estimating density and individual differences
54 Exploring variation across subjects with PCA
55 What have we seen?
56 Technical details
Zooming in on Human Growth
62 Height measurements at three scales
63 Velocity and acceleration
64 An equation for growth
65 Timing or phase variation in growth
66 Amplitude and phase variation in growth
67 What we have seen?
68 Notes and further issues
82 Analyzing shapes without landmarks
83 Investigating shape variation
84 The shape of arthritic bones
842 Regularizing the discriminant analysis
843 Why not just look at the group means?
85 What have we seen?
862 Why is regularization necessary?
863 Crossvalidation in classification problems
Functional Models for Test Items
92 The ability space curve
93 Estimating item response functions
94 PCA of log oddsratio functions
95 Do women and men perform differently on this test?
97 What have we seen?
Predicting Lip Acceleration from Electromyography
102 The lip and EMG curves
103 The linear model for the data
104 The estimated regression function
105 How far back should the historical model go?
106 What have we seen?
The Dynamics of Handwriting Printed Characters
112 An introduction to dynamic models
113 One subjects printing data
114 A differential equation for handwriting
115 Assessing the ﬁt of the equation
116 Classifying writers by using their dynamic equations
117 What have we seen?
A Differential Equation for Juggling
122 The data and preliminary analyses
123 Features in the average cycle
124 The linear differential equation
125 What have we seen?
126 Notes and references
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acceleration curves ADHD arc length arthritic arthritic bones average B-spline B-spline basis basis functions bone shape Chapter coefficients consider coordinate corresponding criminology cross-validation dashed line datum defined density function discriminant analysis distribution dynamic eburnated eigenvalue electromyography estimated examinees F F F F M F func function h(t functional data analysis functional principal components functions Pi handwriting harmonic indicate individual intercondylar notch item response functions juggling cycle landmarks linear differential equation linear discriminant Linear discriminant analysis lip acceleration mean curve measure method mode of variability msec observed osteoarthritis period phase variation phase-plane plot plotted in Figure points positive principal component weight principal components analysis Ramsay and Silverman reaction record registered regression right panel roughness penalty sample shown in Figure shows Silverman 1997 smoothing parameter space curve square standard values varimax vector velocity warping function weight function X-coordinate zero
Page 185 - Growth, Maturation and Body Composition: The Fels Longitudinal Study 1929-1991. Cambridge: Cambridge University Press, 1992.
Page 185 - Ramsay, JO, Bock, RD, and Gasser, T. (1995). Comparison of height acceleration curves in the Fels, Zurich, and Berkeley growth data. Annals of Human Biology, 22, 413-426.