Shifting the Interpretive Framework of Binary Coded Dummy Variables (2003)

ABSTRACT The traditional binary coding scheme is the starting point, and often the ending point, for the coding and interpretation of dummy variable coefficients for qualitative variables in regression analysis. The binary coding scheme produces an interpretive framework for the coefficients that measure the net effect of being in a given category as compared to an omitted category. This may result in coefficients that are as arbitrary as the selection of the omitted categories. Two methods for shifting the binary coded coefficients are presented to assist in establishing a more meaningful interpretive framework. The shifted frameworks allow for interpretation of the coefficients about an of the dependent variable. One method allows for each coefficient to be interpreted as a comparison to the unweighted average of the dependent variable when averaged over all subcategory means. The second method allows for an interpretation of the coefficients to the overall mean of the dependent variable. Since the shifted framework coefficients are compared to an average, the coefficients are insensitive to the omitted categories. The effort to shift the interpretative framework is minimal and can be effected without the use of a computer program. The shifted frameworks can be determined by incorporating alternative coding schemes using a computer program. INTRODUCTION The use of dummy variables to represent qualitative variables in regression analysis has become quite prevalent in introductory business and economic statistics courses (Daniel & Terrell, 1992; Anderson, Sweeney & Williams, 2002). The specific information on coding the dummy variables is typically presented using a binary coding scheme (0,1). The binary scheme assigns members of a particular category for the qualitative variable a code of 1 and members not in that particular category receive a code of 0. Usually, the zero coded category is selected to serve as the reference or comparison point for the interpretation of the regression coefficients. These coefficients will express the difference between a selected category and the reference category for the qualitative variable. The choice of a reference category is arbitrary and may present problems of interpretation. When a number of binary coded qualitative variables are used for a regression model, a reference category for each qualitative variable is selected as the comparison points. The resulting regression coefficients may yield unclear and sometimes awkward interpretations as to which categories have been designated for comparisons. The purpose of this paper is to illustrate processes for shifting the interpretive framework of binary coded regression coefficients. A major reason for the shifting processes is to provide coefficients that lend themselves to more meaningful interpretations. Starting with binary-coded coefficients, usually generated with the assistance of a statistical computer package, the shifting process can be accomplished with or without the assistance of a computer program. The shift in the interpretative framework is such that the contrast of a regression coefficient for a designated category is made to an value for the dependent variable and not to a specified zero coded category. While the shifting processes will yield numerically different coefficients, the overall fit and significance of the regression model remain unchanged. A main advantage of shifting the interpretative framework of binary coded dummy variables to an is that the coefficients are no longer sensitive to which class is treated as the omitted class. FRAMEWORK SHIFTING WITHOUT A COMPUTER PACKAGE The process of shifting the interpretive framework of binary coded coefficients can be made without the use of a computer program by adding a constant, k, to the coefficients within each set of coefficients for a qualitative variable and subtracting k from the regression equation constant or intercept. …