A Shortened Method of Estimation of Mental Factors by Regression

Abstract

A TYPE of problem of estimation with which one meets in the theory of mental factors is this: a team of n tests z_i (i = 1, 2.., n) has been analysed into r common factors f_oa (α = 1, 2, r) and n specifics f_1i, all of which are normalized and uncorrelated, but otherwise unknown. The observed test-scores (in standard measure) can then, in matrix notation, be represented as follows. where the column vectors z, f₀ and f₁ indicate the tests, the common factors and the specifics respectively. The matrices M₀ and M₁ whose elements are the loadings of the tests with the hypothetical factors, are regarded as known. When it is desired to estimate the common factors in terms of the test-scores, the usual regression method leads to the formula: where &fcirc;₀ is the estimate of f₀.