An Examination of an Ecological Model of Neighborhood Change, Which Employs a Biased Estimation Technique

Abstract

The problems created by multicollinearity when estimating a single equation least squares model are well-known. This problem is particularly troublesome in ecological research because of the heavy reliance of this field on census data and other secondary data sources. This paper explores one solution to the problem of multicollinearity in ecological research—ridge regression. Using census-tract data from Cleveland, Ohio for the years 1960–1970, an ecological model, known as the tipping-point model, of neighborhood change, was evaluated. It was determined that multicollinearity was a problem. To minimize the detrimental effects of multicollinearity and to facilitate structural interpretation, the model was reestimated with the ridge regression technique. The result was a total mean square error that was significantly smaller than the total variance resulting from an ordinary least squares solution. Hence, the estimates of the coefficients produced by the ridge regression were closer, on the average, to the true population parameters than the ordinary least squares estimates. Results of the ordinary least squares and ridge regression are presented and discussed and the utility of ridge regression in ecological research is evaluated.