Abstract #301341

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JSM 2003 Abstract #301341
Activity Number: 400
Type: Invited
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics & the Environment
Abstract - #301341
Title: Factor Analysis for Multivariate Spatial Data
Author(s): William F. Christensen*+
Companies: Brigham Young University
Address: Department of Statistics, Provo, UT, 84602,
Keywords: latent variables ; georeferenced data ; kriging
Abstract:

Latent variable models such as the linear factor analysis model have traditionally been popular in the social sciences where researchers are often interested in abstract concepts such as feelings, attitudes, and aptitudes. More recently, factor analysis models have been used in modeling unobservable environmental variables such as soil richness, pollution source contributions, hydrogeological effects, and ecological trends. Factor analysis models treat each observed variable as a linear combination of a smaller number of unobservable common factors plus a unique error. When modeling multivariate spatial data, each of the factors and errors is a spatially correlated process. The validity of statistical inference associated with model parameter estimates depends on the correlation structure of both the factor and error processes. We evaluate the impact of such correlation, discuss scenarios in which standard (i.i.d.) factor analysis methods will yield valid statistical inference, and present an alternative to standard factor analysis for cases in which dependence structure must be directly incorporated.

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