A Dichotomous Behavior of Guttman-Kaiser Criterion from Equi-Correlated Normal Population

نویسندگان

چکیده

We consider a p-dimensional, centered normal population such that all variables have positive variance σ2 and any correlation coefficient between different is given nonnegative constant ρ < 1. Suppose both the sample size n dimension p tend to infinity with p/n → c > 0. prove limiting spectral distribution of matrix Marcenko-Pastur index scale parameter 1 − ρ. By distributions, we rigorously show behavior widespread stopping rules Guttman-Kaiser criterion cumulative-percentage-of-variation rule in PCA andEFA. As result, establish following dichotomous when are large, but small: (1) retains small number for 0, as suggested by Kaiser, Humphreys, Tucker [Kaiser, H. F. (1992). On Cliff’s formula, Kaiser-Guttman factors. Percept. Mot. Ski. 74]; (2) p/2 = simulation study [Yeomans, K. A. Golder, P. (1982). The predictor common J. Royal Stat. Soc. Series D. 31(3)].

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ژورنال

عنوان ژورنال: Journal of the Indonesian Mathematical Society

سال: 2022

ISSN: ['2086-8952', '2460-0245']

DOI: https://doi.org/10.22342/jims.28.3.1158.272-303