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# Boxplots of the 500 mean values of index I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I$$\end{document} obtained for each scenario among simulated patients affected by response shift (in white) and among simulated patients not affected by response shift (in grey). Each pair of boxplots corresponds to one scenario. Subset of scenarios considered: N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} = 200 (sample size), p=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=$$\end{document} 25% (proportion of patients affected by response shift), Δ=-0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta =-0.2$$\end{document} (average change in the latent variable over time); uniform recalibration (UR). RS response shift, J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} number of items, M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M$$\end{document} number of response categories per item

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PurposeMethods for response shift (RS) detection at the individual level could be of great interest when analyzing changes in patient-reported outcome data. Guttman errors (GEs), which measure discrepancies in respondents’ answers compared to the average sample responses, might be useful for detecting RS at the individual level between two time poi...

## Citations

... The four analysis steps pertain to the situation in which a test or questionnaire is administered once to a sample from the population of interest, but in repeated measurement, the issue of response shift-that is, a change in patients' perspective on the meaning of an item-may reveal itself through a change in item ordering at the individual level. In this special section, Dubuy et al. [32] mentioned chronic diseases where patients regularly adapt to their life circumstances, resulting in a different interpretation of items when tested repeatedly. In their contribution to the special section, these authors discuss a method to study this phenomenon of response shift for patient-reported outcomes. ...

We introduce the special section on nonparametric item response theory (IRT) in Quality of Life Research. Starting from the well-known Rasch model, we provide a brief overview of nonparametric IRT models and discuss the assumptions, the properties, and the investigation of goodness of fit. We provide references to more detailed texts to help readers getting acquainted with nonparametric IRT models. In addition, we show how the rather diverse papers in the special section fit into the nonparametric IRT framework. Finally, we illustrate the application of nonparametric IRT models using data from a questionnaire measuring activity limitations in walking. The real-data example shows the quality of the scale and its constituent items with respect to dimensionality, local independence, monotonicity, and invariant item ordering.