Mathematics Physical Sciences Science & Technology Statistics & Probability
Factor analysis is a commonly used method of modelling correlated multivariate exposure data. Typically, the measurement model is assumed to have constant factor loadings. However, from our preliminary analyses of the Environmental Protection Agency's (EPA's) PM2.5 fine speciation data, we have observed that the factor loadings for four constituents change considerably in stratified analyses. Since invariance of factor loadings is a prerequisite for valid comparison of the underlying latent variables, we propose a factor model that includes non-constant factor loadings that change over time and space using P-spline penalized with the generalized cross-validation (GCV) criterion. The model is implemented using the Expectation-Maximization (EM) algorithm and we select the multiple spline smoothing parameters by minimizing the GCV criterion with Newton's method during each iteration of the EM algorithm. The algorithm is applied to a one-factor model that includes four constituents. Through bootstrap confidence bands, we find that the factor loading for total nitrate changes across seasons and geographic regions.
Using a latent variable model with non-constant factor loadings to examine PM2.5 constituents related to secondary inorganic aerosols
Creators
Zhenzhen Zhang - University of Michigan–Ann Arbor
Marie S. O'Neill - University of Michigan–Ann Arbor
Brisa N. Sanchez - University of Michigan–Ann Arbor
Publication Details
Statistical modelling, v 16(2)
Publisher
Sage
Number of pages
23
Grant note
R01ES016932 / NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA; NIH National Institute of Environmental Health Sciences (NIEHS)
RD834800; RD83543601 / EPA; United States Environmental Protection Agency
R01ES016932; R01ES017022; P01ES022844; P20ES018171 / NIH; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA
P30 ES017885 / UM NIEHS Core Center
Resource Type
Journal article
Language
English
Academic Unit
Epidemiology and Biostatistics
Web of Science ID
WOS:000373389000001
Other Identifier
991020100071004721
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Web of Science research areas
Statistics & Probability
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