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psychometrikavol. 80, no. 4, 968994 December 2015doi: 10.1007/s11336-015-9458-9
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Web End = CONSTRAINED DUAL SCALING FOR DETECTING RESPONSE STYLES IN CATEGORICAL DATA
Pieter C. Schoonees, Michel van de Velden and Patrick J. F. Groenen
ERASMUS UNIVERSITY ROTTERDAM
Dual scaling (DS) 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 DS and correspondence analysis literature. It is shown here that a peculiarity of the DS 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 DS 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.
Key words: response style, dual scaling, correspondence analysis, splines, nonnegative least squares, K -means.
1. Introduction
A major issue in questionnaire-based research is the presence of response styles. A response style, sometimes also known as response bias or scale usage heterogeneity, can be described as systematic bias due to a respondents tendency to respond to survey items regardless of its content (Van Rosmalen, Van Herk, & Groenen, 2010). Paraphrasing, a response style is the manner in which a person uses a rating scale, an example being extreme response style where the respondent, for no substantial reason, prefers to use the endpoints of the Likert scale more often than the intermediate rating categories.
Response styles can invalidate statistical analyses since they are completely confounded with the substantial information contained in the data and hence biases results in nontrivial ways (Baumgartner & Steenkamp, 2001). The problem manifests itself when different respondents resort to different response styles within the same data set. Advanced methods, such as the latent-class multinomial logit model of Van Rosmalen et al. (2010), the multidimensional ordinal IRT model of De Jong and Steenkamp (2010), or the ordinal regression model with heterogeneous thresholds of Johnson (2003), have been developed to...