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Constrained Dual Scaling for Detecting Response Styles in Categorical Data.

Schoonees PC, van de Velden M, Groenen PJ - Psychometrika (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands. schoonees@gmail.com.

ABSTRACT
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.

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a Optimal scores assigned to the  response style groups, from rating 1 (left) to rating 9 (right). b Curvature plot similar to Figure 3 for the four groups, with the axes now transformed to obtain a more symmetrical plot. The ellipse in the centre is an approximate 95 % confidence ellipse for no response style.
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Fig11: a Optimal scores assigned to the response style groups, from rating 1 (left) to rating 9 (right). b Curvature plot similar to Figure 3 for the four groups, with the axes now transformed to obtain a more symmetrical plot. The ellipse in the centre is an approximate 95 % confidence ellipse for no response style.

Mentions: Consider the results for groups. These four groups consist of 67, 71, 61 and 69 panellists, respectively. The rating scale usage of these groups are displayed in Figure 10, panels (a)–(d). Figure 11 displays the optimal scores assigned to the ratings in the different groups as well as their curvature chart. The curvature chart includes an approximate 95 % confidence ellipse constructed for the parameter estimates of 5000 data sets simulated under the assumption that no response styles exist. Any group falling outside this band therefore has a significantly nonlinear response mapping and hence a response style.Fig. 10


Constrained Dual Scaling for Detecting Response Styles in Categorical Data.

Schoonees PC, van de Velden M, Groenen PJ - Psychometrika (2015)

a Optimal scores assigned to the  response style groups, from rating 1 (left) to rating 9 (right). b Curvature plot similar to Figure 3 for the four groups, with the axes now transformed to obtain a more symmetrical plot. The ellipse in the centre is an approximate 95 % confidence ellipse for no response style.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4644217&req=5

Fig11: a Optimal scores assigned to the response style groups, from rating 1 (left) to rating 9 (right). b Curvature plot similar to Figure 3 for the four groups, with the axes now transformed to obtain a more symmetrical plot. The ellipse in the centre is an approximate 95 % confidence ellipse for no response style.
Mentions: Consider the results for groups. These four groups consist of 67, 71, 61 and 69 panellists, respectively. The rating scale usage of these groups are displayed in Figure 10, panels (a)–(d). Figure 11 displays the optimal scores assigned to the ratings in the different groups as well as their curvature chart. The curvature chart includes an approximate 95 % confidence ellipse constructed for the parameter estimates of 5000 data sets simulated under the assumption that no response styles exist. Any group falling outside this band therefore has a significantly nonlinear response mapping and hence a response style.Fig. 10

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands. schoonees@gmail.com.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus