“Regression Analysis and Problems of Multicollinearity”

Communications in Statistics - Theory and Methods 01/1975; 4(3):277-292. DOI: 10.1080/03610927308827246


Multicollinearity or linear dependence among the vectors of regressor variables in a multiple linear regression analysis can have sever effects on the estimation of parameters and on variables selection techniques. This expository paper examines the sources of multicollinearity and discusses some of its harmful affects. Several methods proposed in the literature for detecting multicollinearity and dealing with the associated problems are also presented and discussed.

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    • "Even if additional data points can be collected, this may not solve the problem. For a discussion of collinearity, its sources, consequences and solutions, see Mason et al. (1975). "
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    ABSTRACT: Ridge Regression techniques have been found useful to reduce mean square errors of parameter estimates when multicollinearity is present. But the usefulness of the method rest not only upon its ability to produce good parameter estimates, with smaller mean squared error than Ordinary Least Squares, but also on having reasonable inferential procedures. The aim of this paper is to develop asymptotic confidence intervals for the model parameters based on Ridge Regression estimates and the Edgeworth expansion. Some simulation experiments are carried out to compare these confidence intervals with those obtained from the application of Ordinary Least Squares. Also, an example will be provided based on the well known data set of Hald. KeywordsAsymptotic confidence intervals–Collinearity–Edgeworth expansion–Ridge regression
    Full-text · Article · May 2011 · Statistical Papers
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    • "86-96; Johnston 1984, p. N O ) . Multicollinearity is a relative, not an absolute problem and although a variety of collinearity indices are available (Farrar and Glauber 1967; Mason, Gunst, and Webster 1975; Willan and Watts 1978), no single measure has been either widely accepted or shown to completely characterize the problem. Two diagnostic statistics are particularly useful for evaluating the impact of multicollinearity on estimates of structural coefficients in simultaneous-equation models: (1) the variance inflation factor and (2) condition indexes and associated regression coefficient variance decomposition. "
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    ABSTRACT: Simultaneous-equation statistical models are an attractive method for directly analyzing interactions among components of geomorphic systems. This study demonstrates that the utility of simultaneous-equation analysis is limited for fluvial systems by inherent multicollinearity among hydrologic and morphologic variables. Although multicollinearity for observed data may not be severe, estimation procedures for simultaneous-equation models often enhance this multicollinearity to problematic levels. Diagnostic tests are applied to three models of fluvial systems to illustrate the severity of the problem. It is recommended that investigators who develop simultaneous-equation models perform appropriate diagnostic evaluations to determine the impact of multicollinearity on specific parameter estimates.
    Preview · Article · Sep 2010 · Geographical Analysis
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    ABSTRACT: The Internet is a global and borderless environment, and it will be a challenge having to identify and trust the other party whom one is transacting with. Developing and communicating trustworthiness to one's business partners is crucial at a time when business opportunities in e-commerce are flourishing. The objective of this study is to examine the role that trust plays and the extent to which it drives business-to-business e-commerce participation in Singapore. Indeed, knowledge of the role of trust, in its specific dimensions, will be useful to businesses in meeting the future competitive pressures surrounding it in the e- commerce context. Trading partner trust and electronic trust are examined as the independent variables of participation. The results demonstrated that both trading partner trust
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