Constrained Dual Scaling for Detecting Response Styles in Categorical Data

Dual scaling is a multivariate exploratory method equivalent to correspondence analysis when analysing contingency tables. However, for the analysis of rating data different proposals appear in the dual scaling and correspondence analysis literature. It is shown here that a peculiarity of the dual scaling method can be exploited to detect differences in response styles. Response styles occur when respondents use rating scales differently for reasons not related to the questions, often biasing results. A spline-based constrained version of dual scaling is devised which can detect the presence of four prominent types of response styles, and is extended to allow for multiple response styles. An alternating nonnegative least squares algorithm is devised for estimating the parameters. The new method is appraised both by simulation studies and an empirical application.