著者

小笠原 春彦 OGASAWARA Haruhiko

出版者

The Behaviormetric Society of Japan

雑誌

行動計量学 (ISSN:03855481)

巻号頁・発行日

vol.23, no.2, pp.122-129, 1996

被引用文献数

7

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The varimax rotation, a special case of the orthomax method, usually contains the process of normalization by the communalities of manifest variables. After rotation, factor loadings are re-scaled so that the communalities have original values. Although the standard errors of rotated factor-loadings have been discussed from the general view point of estimation of parameters with restrictions, the actual standard errors for normalized rotation have not been provided. In this paper a method of estimating the asymptotic standard errors in the normalized orthomax rotation is given. Two artificial examples are provided in which standard errors become extremely large with or without normalization.

著者

Ogasawara Haruhiko

出版者

日本行動計量学会

雑誌

Behaviormetrika (ISSN:03857417)

巻号頁・発行日

vol.32, no.1, pp.9-28, 2005-01

被引用文献数

1

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Formulas for the asymptotic biases of the estimators of the normal theory standard errors in factor analysis are given with and without the assumption of multivariate normality for observed variables. The biases are derived from the asymptotic variances of standard error estimators and the asymptotic biases of the estimated variances of parameter estimators. The latter biases are derived from the asymptotic variances/covariances and asymptotic biases of the parameter estimators. The formulas cover the cases for unstandardized and standardized variables. Numerical examples using factor analysis models show the accuracy of the formulas. The biases of standard error estimators are theoretically and empirically shown to be of the same order as that of the differences between the asymptotic standard errors neglecting higher-order terms and those considering them.