Transparent aggregation of variables with Individual Differences Scaling

Abstract

Although the aggregation of many linguistic variables has provided new insights into the structure of language varieties, aggregation studies have been criticized for obscuring the behavior of individual input variables. Previous solutions to this criticism consisted of extensive post-hoc calculations, simple correlation measures, or highly complex algorithms. We think that these solutions can be improved. Therefore, the current article proposes a creative use of Individual Differences Scaling (INDSCAL) as an alternative, more straightforward solution. INDSCAL is a branch of Multidimensional Scaling, which is currently the preferred dimension reduction technique for most aggregation studies. The link to the existing methodology and the simplicity of its rationale are the main advantages of INDSCAL. The article introduces INDSCAL by means of a non-linguistic example, a discussion of the mathematical properties, and a case study on the lexical convergence between Belgian and Netherlandic Dutch in a corpus of language from 1950 and 1990. The case study shows how INDSCAL reproduces the results of a typical aggregation study, but elegantly keeps open the possibility of investigating the behavior of individual variables.