15 Analysis of ordered categorical data through appropriate scaling

Publisher Summary Common to both the social and life sciences, research and survey data are often collected in a categorical form. The categories may be nominal as in the case of food group, sex, and race, or they may have underlying continua, such as weight (categorized as underweight, average, or overweight) and 'height' (categorized as tall, average, or short). These ordered categories are used in the place of their corresponding continuous scales, “weight in pounds” or “height in inches” for convenience in collecting data, especially when the underlying quantity cannot be easily ascertained. By using the proposed method for rescaling, the arbitrarily ordered categories are changed into real points on a scale and stronger inferences can be made because the differences of the magnitudes among points are known. This general procedure does not ensure that when the row or column categories have an order structure, the corresponding estimated quantitative scores are similarly ordered. If this does not happen, statistical analysis based on estimated quantitative scores may not have a meaningful interpretation. The problem of rescaling or assigning quantitative scores to the row and column categories of a contingency table has received considerable attention in recent times. The scores are usually obtained by maximizing a chosen criterion, such as the correlation coefficient between row and column categories.