絶対誤差総和最小化原理による擬直交および斜交基本因子回転基準について

柏木 繁男; 石塚 智一

doi:10.4992/jjpsy.45.287

A PSEUDO-ORTHOGONAL AND AN OBLIQUE PRIMARY FACTOR ROTATION CRITERIA BASED ON THE PRINCIPLE OF MINIMIZING THE SUM OF ABSOLUTE ERRORS (MSAE)

SHIGEO KASHIWAGI, TOMOICHI ISHIZUKA

Author information

JOURNAL FREE ACCESS

1975 Volume 45 Issue 6 Pages 287-299

DOI https://doi.org/10.4992/jjpsy.45.287

Details

Published: February 10, 1975 Received: May 30, 1974 Available on J-STAGE: July 16, 2010 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: July 16, 2010 Reason for correction: - Correction: ABSTRACT Details: Wrong : A pseudo-orthogonal and an oblique primary factor rotation criteria which were based on the principle of minimizing the sum of absolute errors (MSAE) were proposed in some modified extensions of the orthogonal case of Kashiwagi (1965)'s geomax criterion to the oblique ones. The principles of single plane rotation consisted of the following two kinds of classification procedures. The first one of them was common to both criteria. That is, an initial orthogonal factor matrix (3-1) or (3-1*) was transformed orthogonally by the objective function (3-3) which aimed to attain the minimum value of the sum of the absolute elements in the second factor of the resulting factor matrix (3-2). The minimum value was seeked through the explorative computational procedures (2-8) to (2-12).
The second classification procedure differed from the pseudo-orthogonal (MSAE Pseudo-Orthogonal) primary factor rotation criterion to the oblique primary factor (MSAE Oblique Primary Factor) rotation one. While the MSAE Pseudo-Orthogonal factor rotation was carried out with the objections functions (3-7ω₁) and (3-7ω₂′) which aimed to attain the minimum values of the absolute sums in (3-6) derived from (3-2**), the MSAE Oblique Primary factor rotation was carried out with the objective functions (3-10ω₁) and (3-10ω₂) which aimed to attain the minimum values of the sums in the second factors in both (_πb_K1πb_K2) and (_νb_k1νb_k2). The way of seeking the minimum was the same explorative computational procedures mentioned above. Here note that (_πb_K1πb_K2) which belonged to the first and third quadrants and (_νb_k1νb_k2) which belonged to the second and fourth quadrants were the submatrices in (3-2*) instead of (3-2**).
Several numerical examples including the famous artificial 20 and 26 box problems of Thurstone (1947) were tested by two kinds of the proposed oblique primary factor rotation criteria, and the results presented in Table 1 to Table 4 showed excellent fit to the subjective judgements in the original studies.
Right : A pseudo-orthogonal and an oblique primary factor rotation criteria based on the principle of minimizing the sum of absolute errors (MSAE) are proposed. As a revised form of Kashiwagi (1965)'s geomax criterion, the orthogonal factor rotation criterion based on the principle of MSAE is discussed so as to give a preliminary guide to our present proposals. The principles of the pseudo-orthogonal and the oblique primary factor rotation. criteria are explained in the extensive forms of the orthogonal case to the oblique ones. The proposed criteria are applied to several numerical examples including two kinds of Thurstone (1947)'s box problems and it is shown that they reproduce almost perfectly the psychological assumptions in the original studies.

Abstract

A pseudo-orthogonal and an oblique primary factor rotation criteria based on the principle of minimizing the sum of absolute errors (MSAE) are proposed. As a revised form of Kashiwagi (1965)'s geomax criterion, the orthogonal factor rotation criterion based on the principle of MSAE is discussed so as to give a preliminary guide to our present proposals. The principles of the pseudo-orthogonal and the oblique primary factor rotation. criteria are explained in the extensive forms of the orthogonal case to the oblique ones. The proposed criteria are applied to several numerical examples including two kinds of Thurstone (1947)'s box problems and it is shown that they reproduce almost perfectly the psychological assumptions in the original studies.

Corresponding author

Correction information

Register with J-STAGE for free!