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On the empirical equivalence of regression components and common factors
Author(s) -
Steiger James H.
Publication year - 1980
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.2044-8317.1980.tb00608.x
Subject(s) - mathematics , equivalence (formal languages) , factor regression model , factor analysis , regression analysis , regression , statistics , econometrics , factor (programming language) , component (thermodynamics) , set (abstract data type) , polynomial regression , discrete mathematics , proper linear model , computer science , physics , thermodynamics , programming language
Schönemann & Steiger (1976, Theorem 5) proved that the common factor model fits a given set of observed variables if and only if a restricted regression component model fits the same variables. In the present paper a number of results, relating factor score estimates and the class of all sets of ‘factor‐equivalent’ regression components, are presented. These results clarify and extend a result given by McDonald (1977).