A Class of Population Covariance Matrices in the Bootstrap Approach to Covariance Structure Analysis

Multivariate Behavioral Research
Ke-Hai YuanHirokazu Yanagihara

Abstract

Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given sample size, also provides more accurate results than those based on standard asymptotics. But the procedure needs a matrix to play the role of the population covariance matrix. The closer the matrix is to the true population covariance matrix, the more valid the bootstrap inference is. The current paper proposes a class of covariance matrices by combining theory and data. Thus, a proper matrix from this class is closer to the true population covariance matrix than those constructed by any existing methods. Each of the covariance matrices is easy to generate and also satisfies several desired properties. An example with nine cognitive variables and a confirmatory factor model illustrates the details for creating population covariance matrices with different misspecifications. When evaluating the substantive model, bootstrap or simulation procedures based on these matrices will lead to mo...Continue Reading

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Citations

May 23, 2019·Journal of Advanced Nursing·Tae Yamaguchi, Ikuko Sakai
Dec 7, 2019·Multivariate Behavioral Research·Chuchu Cheng, Hao Wu
Jan 31, 2020·Ecology·Mallarie E YeagerA Randall Hughes
Jun 28, 2017·Structural Equation Modeling : a Multidisciplinary Journal·Gitta H LubkeStéphanie M van den Berg
Jan 6, 2021·Multivariate Behavioral Research·Ke-Hai YuanKaterina M Marcoulides

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Software Mentioned

CSA
SAS IML
Splus
LISREL
SEM
Matlab

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