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Treatment of ‘don’t know’ responses in a mixture model for rating data

Listed author(s):
  • Marica Manisera


    (University of Brescia)

  • Paola Zuccolotto


    (University of Brescia)

Registered author(s):

    Abstract In recent years the use of questionnaires to investigate and measure human perceptions has hugely intensified and, correspondingly, there has been an increased need for statistical models able to treat ordered categorical data, that usually derive from questions asking for ratings. In this paper we focus on a specific class of models, called Combination of Uniform and shifted Binomial (CUB), based on the assumption that rating data derive from an unconscious decision process composed of two independent components, called feeling and uncertainty. More precisely, we deal with a recently proposed extension in this context, the Nonlinear CUB model, which beyond being able to measure feeling and uncertainty, gives an idea of the state of mind of respondents toward the scale used to express the ratings. The aim of the paper is to show how the parameters of the Nonlinear CUB model can be adjusted in order to take account of the presence of ‘don’t know’ responses, following a recent idea developed in the CUB context. In addition, a graphical representation is proposed, able to summarize all the results in a unique graph. A case study is presented, concerned with data from the Eurobarometer survey.

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    Article provided by Springer & Sapienza Università di Roma in its journal METRON.

    Volume (Year): 74 (2016)
    Issue (Month): 1 (April)
    Pages: 99-115

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    Handle: RePEc:spr:metron:v:74:y:2016:i:1:d:10.1007_s40300-015-0075-2
    DOI: 10.1007/s40300-015-0075-2
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    1. Maria Iannario, 2010. "On the identifiability of a mixture model for ordinal data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 87-94.
    2. Romina Gambacorta & Maria Iannario, 2013. "Measuring Job Satisfaction with CUB Models," LABOUR, CEIS, vol. 27(2), pages 198-224, June.
    3. D'Elia, Angela & Piccolo, Domenico, 2005. "A mixture model for preferences data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 917-934, June.
    4. Leonardo Grilli & Maria Iannario & Domenico Piccolo & Carla Rampichini, 2014. "Latent class CUB models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 105-119, March.
    5. Maria Iannario & Marica Manisera & Domenico Piccolo & Paola Zuccolotto, 2012. "Sensory analysis in the food industry as a tool for marketing decisions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(4), pages 303-321, December.
    6. Frederic Lord, 1983. "Maximum likelihood estimation of item response parameters when some responses are omitted," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 477-482, September.
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