A paired comparison approach for the analysis of sets of Likert-scale responses

Abstract

Summary. This paper provides an alternative methodology for the analysis of a set of Likert responses measured on a common attitudinal scale when the primary focus of interest is on the relative importance of items in the set. The method makes fewer assumptions about the distribution of the responses than the more usual approaches such as comparisons of means, MANOVA or ordinal data methods. The approach transforms the Likert responses into paired comparison responses between the items. The complete multivariate pattern of responses thus produced can be analysed by an appropriately reformulated paired comparison model. The dependency structure between item responses can also be modelled flexibly. The advantage of this approach is that sets of Likert responses can be analysed simultaneously within the Generalized Linear Model framework, providing standard likelihood based inference for model selection. This method is applied to a recent international survey on the importance of environmental problems.

Assortative mating on risk attitude

“…A second potential problem with the analysis of self-reported risk is the possibility of measurement error: Likert-scale responses are dictated partly by the "response style" of respondents. Here, we appeal to Dittrich et al (2007) who establish that to include a random-effects component, as we do in our model, is sufficient to capture inter-respondent differences in response style.…”

prefmod: AnRPackage for Modeling Preferences Based on Paired Comparisons, Rankings, or Ratings

“…Sometimes, the Likert-type responses are treated as categorical, where frequencies of the high categories for each item are used to determine a ranking of the items. A detailed discussion is given in Dittrich, Francis, Hatzinger, and Katzenbeisser (2007).…”

“…The number of possible patterns for real PCs including an undecided category is 3 ( J 2 ) whereas there are fewer derived patterns for rating data since several rating patterns have the same representation as derived PC patterns (e.g., the rating patterns (1, 1, 2) and (2,2,3) are both represented by the unique PC pattern (0, 1, 1)). For details see Dittrich, Francis, Hatzinger, and Katzenbeisser (2007).…”

Subject-specific Bradley–Terry–Luce models with implicit variable selection

“…The adjacent categories BTL model can also be represented as a log-linear model, which has been extensively discussed in the literature (see Agresti, 1992;Dittrich et al, 1998;Dittrich et al, 2004;Dittrich et al, 2007). When the response consists of K = 2 categories, the binary BTL model (1) is a special case of the cumulative BTL model (4) and the adjacent categories BTL model (7).…”