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Asymptotic biases of the unrotated/rotated solutions in principal component analysis
Author(s) -
Ogasawara Haruhiko
Publication year - 2004
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.2004.tb00143.x
Subject(s) - mathematics , principal component analysis , multivariate statistics , asymptotic distribution , computation , normality , statistics , multivariate normal distribution , econometrics , estimator , algorithm
Asymptotic biases of the parameter estimates in principal component analysis with substantial misspecification are derived. The solutions for unstandardized and standardized observed variables are considered with and without orthogonal and oblique rotations. The distribution of observed variables can be non‐normal as long as the finite fourth‐order moments of the observed variables exist. When multivariate normality holds for the observed variables, substantial reduction of the amount of computation can be achieved. Numerical examples with simulations are given, with some discussion on the tendency of the biases to reduce the absolute values of parameter estimates.