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PLoS One. 2012;7(6):e38923. doi: 10.1371/journal.pone.0038923. Epub 2012 Jun 19.

Visualizing rank deficient models: a row equation geometry of rank deficient matrices and constrained-regression.

Author information

1
Department of Sociology, University of Oregon, Eugene, Oregon, USA. bobrien@uoregon.edu

Abstract

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency.

PMID:
22723906
PMCID:
PMC3378569
DOI:
10.1371/journal.pone.0038923
[Indexed for MEDLINE]
Free PMC Article
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