Model estimation using ridge regression with the variance normalization criterion

Lee, Wan-Fung (1979) Model estimation using ridge regression with the variance normalization criterion. Masters thesis, Memorial University of Newfoundland.

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Abstract

Structural equation model building has been extensively used in the social sciences. The ordinary least squares (OLS) regression technique has been the standard technique used in the single equation method of estimation. OLS regression estimates are erroneous, however, due to the presence of multicollinearity which is attributable to an absence of control over the survey data and to an intrinsic property of structural equation models. The inadequacy of the OLS regression technique when applied to ill-conditioned data was discussed in chapter II. -- Ridge regression, developed by Hoerl and Kennard (1970), is the most promising technique for coping with the multicollinearity problem. However, the technique is inadmissible due to the stochasticity of the estimation criterion. An exposition of ridge regression theory was given in chapter III. In chapter IV, the dilemma of ridge regression was analyzed and a new criterion, called the variance normalization criterion was developed. With this criterion all the difficulties encountered by Hoerl and Kennard’s version of ridge regression are avoided. -- In chapter V, simple ridge regression with the variance normalization criterion was applied to a 5-stage human capital problem which used the Malmo data. Through this example and through the theoretical arguments discussed in chapter II, III, and IV, the following goals of the study were achieved: (1) the superiority of simple ridge regression over ordinary least square regression was demonstrated, (2) Hoerl and Kennard’s version of ridge regression was modified in order to achieve more satisfactory results; and (3) it was demonstrated that simple ridge regression with the variance normalization criterion is superior both to ridge regression estimation procedures using the mean square error criterion and the OLS procedure.

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