Functional Data Analysis

Presented: August 16th, 2005

Speakers: Jim Ramsay, McGill University and Michael O'Connell, Insightful Corporation

Listen to the archived Web cast.

Helpful Links:

• Download the presentation file. [PDF]
  
  
• Download the S+FDA Library: This library for S-PLUS for Windows 7.0 provides methods for transforming longitudinal or spatial data to a smoothed functional form. The goal is to analyze a sample of functions instead of a sample of points. Advantages are that it can handle irregularly spaced data, or data with missing values. Also, calculating derivatives and integrals may provide better information (e.g. graphical) than the original data itself. Tools include linear differential operators, integration, inner product, smoothing, and registration. Analyses supported include linear regression, generalized linear models, principal components, canonical correlation, principal differential analysis, and clustering. Available for Windows only. E-mail us at functional-beta@insightful.com for latest
  S-PLUS 7 library
  
  
• Books by Jim Ramsay:
  • S+Functional Data Analysis User's Guide
    Clarkson, D.; Fraley, C.; Gu, C.; Ramsay, J.
    Springer-Verlag, New York, NY
    ISBN: 0-387-24969-9
  • Applied Functional Data Analysis Methods and Case Studies
    Ramsay, J.O., Silverman, B.W.
    2002, X, 190 p. 112 illus., Softcover
    ISBN: 0-387-95414-7
  • More books on S-PLUS and data analysis
    

Abstract: Functional data analysis involves analysis of data/measurements as functions or curves, rather than analysis of individual data points. In many applications, data measurements are best considered as functions, even when data are gathered at a relatively few number of points. Functional data arise in many fields of research including growth rates, health status indicators, tumor sizes, weather changes, and stock prices.

In this Web cast, we will review two examples of functional data: Height measurements for samples of girls and boys, and a single long series of values of an economic indicator. Our first task will be smoothing, which is the estimation of a smooth function for each set of discrete data values. Once the data are smoothed, we move to some typical functional data analyses, such as the display of descriptive functional statistics, principal components analysis, and functional linear regression.

The goal is to provide a first glimpse of functional data analyses by using the latest version of S-PLUS. In addition, we will explain concepts such as basis functions, smoothing, and object oriented programming techniques. A reference for this Web cast is D. B. Clarkson, C. Fraley, C. C. Guy and J. O. Ramsay (2005) S+Functional Data Analysis User's Guide. New York: Springer.

Presenter Information

Jim Ramsay earned a Ph.D. from Princeton University in 1966 in quantitative psychology, and a B.Ed. at the University of Alberta in 1964. After a year as lecturer at University College London, he joined the Department of Psychology at McGill University, Montreal, Quebec, Canada, where he remains. He also has an Associate Membership in the Department of Mathematics and Statistics at McGill. He has contributed research on various topics in psychometrics, including multidimensional scaling and test theory. His current research focus is on functional data analysis, which involves developing methods for analyzing samples of curves and images. Ramsay and Silverman (1997), Functional Data Analysis, is the first book in this new area, and has been followed up by a book of case studies, Ramsay and Silverman (2002), Applied Functional Data Analysis. He has been President of the Psychometric Society and the Statistical Society of Canada. He received the Gold Medal of the Statistical Society of Canada in 1998.