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Multiple regression and poorly conditioned matrices
Author(s) -
Maxwell A. E.
Publication year - 1977
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.2044-8317.1977.tb00741.x
Subject(s) - regression , mathematics , stability (learning theory) , regression analysis , statistics , linear regression , margin (machine learning) , ridge , econometrics , computer science , machine learning , geography , cartography
The way in which poorly conditioned matrices can adversely affect the stability of estimates of partial regression coefficients is described. It is noted that in the absence of measurement error in the independent variables relative stability can be achieved by the ‘ridge regression’ method, but when the margin of error is considerable, as is generally the case in social science research, poorly conditioned matrices of an extreme kind occur only infrequently. Whether or not they occur the method of estimating regression coefficients which employs the basic model of factor analysis effectively circumvents inherent difficulties.