AN AD HOC PROCEDURE FOR REDUCING THE NUMBER OF VARIABLES TO BE INCLUDED IN A LINEAR MODEL

In explaining phenomena in the social sciences, theory almost always supplies more admissible hypotheses than statistical procedures such as multiple regression analysis can accommodate without degeneration of estimates due to multicollinearity. In the case of a linear model that is being estimated by the least-squares technique, the inclusion of strongly related independent variables results in multicollinearity, causing problems in determining the relative influence of the explanatory variables. This paper presents an ad hoc procedure for reducing the number of variables that are included in a model while preserving structural integrity of the theoretical model. The procedure is applied to an economic development research problem. A limited number of variables were chosen from a larger set of variables using a grouped-variable technique.The paper identifies some elements accounting for the outlays by the Economic Development Administration to generate jobs through industrial development projects. MULTICOLLINEARITY Multicollinearity involves the existence of a linear relationship among the explanatory variables. When an exactly linear or nearly linear relationship exists, it is difficult to estimate the parameters associated with the explanatory variables in regression analysis. Coefficient estimates are unstable and standard errors of the coefficients are large (1, p. 153). When multicollinearity is present, removing from the regression one of two or more highly correlated variables does not markedly reduce the proportion of variance in the dependent variable accounted for. Eliminating some of the independent variables, obtaining new data, or utilizing a priori information concerning the coefficients are possible solutions to the problem. The last two methods were judged to be unsatisfactory for this study. This paper relates how variables were grouped into closely related sets and how one of these variables was chosen as a representative from the homogeneous group so that the effect of this most significant variable (i.e. the variable that most effectively conveys the influence of that group of variables on the dependent variable) is not unduly distorted because of multicollinearity problems.