NCJ Number
85337
Date Published
1981
Length
27 pages
Annotation
This essay first examines multicollinearity, its causes, its identification, and its impact on the ordinary least squares regression model, and then minimization of the effects of multicollinearity is considered, with special attention to biased regression methods.
Abstract
Multicollinearity occurs when two or more predictor variables repeat information. Multicollinearity arises from three principal sources: (1) the overdefined model that occurs when the number of predictors equals or exceeds the number of observations, (2) physically or structurally constrained models, and (3) sampling deficiencies. Multicollinearities can have damaging effects on ordinary least squares methodology, because they can produce misleading and even erroneous inferences. Biased regression techniques such as ridge regression, principal component (PC) regression, and latent root regression (LR) are alternatives to least squares, particularly in the presence of multicollinear data. Such techniques, despite their lack of certain distributional properties, can provide more realistic parameter estimates and are generally more precise than their least squares counterparts. If the multicollinearity is predictive, the LR procedure is recommended; however, when the multicollinearity is nonpredictive, any of the three biased regression techniques can be used. In the latter situation, the choice will depend on many factors, including the technique used for the selection of a ridge parameter or the deletion of the latent roots and latent vectors, the availability of computer algorithms for computing the coefficient estimates, and the purposes of the analysis. Findings are derived from an analysis of data on the availability of firearms in accounting for the variations in the homicide rate of one city. Tabular data and 41 references are provided.