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The maximum‐likelihood solution in inter‐battery factor analysis
Author(s) -
Browne M. W.
Publication year - 1979
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.2044-8317.1979.tb00753.x
Subject(s) - mathematics , canonical correlation , maximum likelihood , statistics , likelihood ratio test , battery (electricity) , restricted maximum likelihood , thermodynamics , physics , power (physics)
Maximum‐likelihood estimates in closed form are derived for Tucker's (1958) inter‐battery factor analysis model. The estimates of inter‐battery factor loadings may be computed by rescaling correlation coefficients between the original variables and the canonical variables obtained in canonical correlation analysis. It is shown that the likelihood ratio test for the number of inter‐battery factors is identical to Bartlett's (1938) test for the number of non‐zero canonical correlations. An alternative approach analogous to the maximum determinant approach of Howe (1955) and Bargmann (1957) is seen to yield the same solution as that obtained by maximum likelihood. The question of rotation of factors is discussed and an example is given.