Constrained Dual Scaling for Detecting Response Styles in Categorical Data.
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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.
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Affiliation: Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands. schoonees@gmail.com.
ABSTRACT
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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. Related in: MedlinePlus |
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Mentions: The basis functions and in (7), as depicted in Figure 2, are piecewise quadratic, with only two of them nonconstant in each of the intervals and . This is convenient because it means the second derivative of , and hence the curvature, depends only on two parameters in each interval. Rescaling without loss of generality so that and , the curvature of (not necessarily defined at ) is given by9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{d^{2}}{dx^{2}} f(x) = {\left\{ \begin{array}{ll} - 8 \alpha _{1} + 4\alpha _{2}, &{}\text {if}\quad 0 \le x < 1/2;\\ - 4\alpha _{2} + 8\alpha _{3}, &{}\text {if}\quad 1/2 < x \le 1;\\ \end{array}\right. } \end{aligned}$$\end{document}d2dx2f(x)=-8α1+4α2,if0≤x<1/2;-4α2+8α3,if1/2<x≤1;Fig. 2 |
View Article: PubMed Central - PubMed
Affiliation: Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands. schoonees@gmail.com.