A General Unfolding IRT Model for Multiple Response Styles

Chen Wei Liu*, Wen Chung Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


It is commonly known that respondents exhibit different response styles when responding to Likert-type items. For example, some respondents tend to select the extreme categories (e.g., strongly disagree and strongly agree), whereas some tend to select the middle categories (e.g., disagree, neutral, and agree). Furthermore, some respondents tend to disagree with every item (e.g., strongly disagree and disagree), whereas others tend to agree with every item (e.g., agree and strongly agree). In such cases, fitting standard unfolding item response theory (IRT) models that assume no response style will yield a poor fit and biased parameter estimates. Although there have been attempts to develop dominance IRT models to accommodate the various response styles, such models are usually restricted to a specific response style and cannot be used for unfolding data. In this study, a general unfolding IRT model is proposed that can be combined with a softmax function to accommodate various response styles via scoring functions. The parameters of the new model can be estimated using Bayesian Markov chain Monte Carlo algorithms. An empirical data set is used for demonstration purposes, followed by simulation studies to assess the parameter recovery of the new model, as well as the consequences of ignoring the impact of response styles on parameter estimators by fitting standard unfolding IRT models. The results suggest the new model to exhibit good parameter recovery and seriously biased estimates when the response styles are ignored.

Original languageEnglish
Pages (from-to)195-210
Number of pages16
JournalApplied Psychological Measurement
Issue number3
Publication statusPublished - 2019 May 1
Externally publishedYes


  • Bayesian statistics
  • multidimensional item response theory
  • response styles
  • unfolding models

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)


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