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Bootstrap scree tests: A Monte Carlo simulation and applications to published data
Author(s) -
Hong Sungjin.,
Mitchell Stephen K.,
Harshman Richard A.
Publication year - 2006
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 - 10.1348/000711005x66770
Subject(s) - parametric statistics , statistics , statistical hypothesis testing , econometrics , monte carlo method , eigenvalues and eigenvectors , nonparametric statistics , mathematics , principal component analysis , goodness of fit , computer science , quantum mechanics , physics
A non‐parametric procedure for Cattell's scree test is proposed, using the bootstrap method. Bentler and Yuandeveloped parametric tests for the linear trend of scree eigenvalues in principal component analysis. The proposed method is for cases where parametric assumptions are not realistic. We define the break in the scree trend in several ways, based on linear slopes defined with two or three consecutive eigenvalues, or all eigenvalues after the k largest. The resulting scree test statistics are evaluated under various data conditions, among which Gorsuch and Nelson's bootstrap CNG performs best and is reasonably consistent and efficient under leptokurtic and skewed conditions. We also examine the bias‐corrected and accelerated bootstrap method for these statistics, and the bias correction is found to be too unstable to be useful. Using seven published data sets which Bentler and Yuan analysed, we compare the bootstrap approach to the scree test with the parametric linear trend test.