Maximizing rating scale information

Rating scale categories should be well defined, mutually exclusive, univocal and exhaustive (J.P. Guilford), but this is not enough. They must also be clearly differentiated in the behavior of the respondents, otherwise more categories do not mean more information. Here is an apparently well constructed scale:

How much do you fear...
1. Not at all
2. A little
3. Somewhat
4. More
5. A lot

But could the respondents clearly discriminate 5 levels of fear? The plot shows the statistical separation of the respondents obtained when adjacent categories are clumped together. Person separation is best with the categories grouped into 3 levels, and one of the dichotomizations is almost as good as the original five category scale. The choice of scoring model can dramatically alter results. The statistically best scoring model for these data was:

How much do you fear...
1. Not at all
2. A little
3. Somewhat, More, A lot

Mark Stone & Ben Wright

Maximizing rating scale information. Stone MH, Wright BD. … Rasch Measurement Transactions, 1994, 8:3 p.386

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Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
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Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
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