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Erschienen in: Advances in Data Analysis and Classification 2/2016

01.06.2016 | Regular Article

Varying uncertainty in CUB models

verfasst von: Anna Gottard, Maria Iannario, Domenico Piccolo

Erschienen in: Advances in Data Analysis and Classification | Ausgabe 2/2016

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Abstract

This paper presents a generalization of a mixture model used for the analysis of ratings and preferences by introducing a varying uncertainty component. According to the standard mixture model, called CUB model, the response probabilities are defined as a convex combination of shifted Binomial and discrete Uniform random variables. Our proposal introduces uncertainty distributions with different shapes, which could capture response style and indecision of respondents with greater effectiveness. Since we consider several alternative specifications that are nonnested, we suggest the implementation of a Vuong test for choosing among them. In this regard, some simulation experiments and real case studies confirm the usefulness of the approach.

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Literatur
Zurück zum Zitat Atkinson A (1970) A method for discriminating between models. J R Stat Soc Ser B 32:323–353MATH Atkinson A (1970) A method for discriminating between models. J R Stat Soc Ser B 32:323–353MATH
Zurück zum Zitat Baumgartner H, Steenback J-B (2001) Response styles in marketing research: a cross-national investigation. J Market Res 38:143–156CrossRef Baumgartner H, Steenback J-B (2001) Response styles in marketing research: a cross-national investigation. J Market Res 38:143–156CrossRef
Zurück zum Zitat Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57(1):289–300MathSciNetMATH Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57(1):289–300MathSciNetMATH
Zurück zum Zitat Buckley J (2009) Cross-national response styles in international educational assessments: evidence from pisa 2006. Technical report, Department of Humanities and Social Sciences in the Professions Steinhardt School of Culture, Education, and Human Development New York University Buckley J (2009) Cross-national response styles in international educational assessments: evidence from pisa 2006. Technical report, Department of Humanities and Social Sciences in the Professions Steinhardt School of Culture, Education, and Human Development New York University
Zurück zum Zitat Cliff N, Keats JA (2003) Ordinal measurement in the behavioral science. Taylor & Francis, UK Cliff N, Keats JA (2003) Ordinal measurement in the behavioral science. Taylor & Francis, UK
Zurück zum Zitat Corduas M, Iannario M, Piccolo D (2009) A class of statistical models for evaluating services and performances. In: Bini M et al (eds) Statistical methods for the evaluation of educational services and quality of products. Contributions to statistics. Springer, New York, pp 99–117 Corduas M, Iannario M, Piccolo D (2009) A class of statistical models for evaluating services and performances. In: Bini M et al (eds) Statistical methods for the evaluation of educational services and quality of products. Contributions to statistics. Springer, New York, pp 99–117
Zurück zum Zitat Cox D (1961) Tests of separate families of hypotheses. In: Proceeding of the fourth Berkeley symposium on mathematical statistics and probability, vol 1, pp 105–123 Cox D (1961) Tests of separate families of hypotheses. In: Proceeding of the fourth Berkeley symposium on mathematical statistics and probability, vol 1, pp 105–123
Zurück zum Zitat Cox D (1962) Further results on tests of separate families of hypotheses. J R Stat Soc Ser B 24:406–424MathSciNetMATH Cox D (1962) Further results on tests of separate families of hypotheses. J R Stat Soc Ser B 24:406–424MathSciNetMATH
Zurück zum Zitat Cox D (2013) A return to an old paper: tests of separate families of hypotheses. J R Stat Soc Ser B (Stat Methodol) 75:207–215MathSciNetCrossRef Cox D (2013) A return to an old paper: tests of separate families of hypotheses. J R Stat Soc Ser B (Stat Methodol) 75:207–215MathSciNetCrossRef
Zurück zum Zitat D’Elia A (2000) The paired comparison mechanism in ranking models: statistical developments and critical issues (in Italian). Quaderni di Statistica 2:173–203 D’Elia A (2000) The paired comparison mechanism in ranking models: statistical developments and critical issues (in Italian). Quaderni di Statistica 2:173–203
Zurück zum Zitat Eid M, Zickar M (2007) Detecting response styles and faking in personality and organizational assessments by mixed rasch models. In: von Davier M, Carstensen CH (eds) Multivariate and mixture distribution rasch models extensions and applications. Statistics for social and behavioral sciences. Springer, Berlin, pp 255–270 Eid M, Zickar M (2007) Detecting response styles and faking in personality and organizational assessments by mixed rasch models. In: von Davier M, Carstensen CH (eds) Multivariate and mixture distribution rasch models extensions and applications. Statistics for social and behavioral sciences. Springer, Berlin, pp 255–270
Zurück zum Zitat Gollwitzer M, Eid M, Jürgensen R (2005) Response styles in the assessment of anger expression. Psychol Assessm 17:56–69CrossRef Gollwitzer M, Eid M, Jürgensen R (2005) Response styles in the assessment of anger expression. Psychol Assessm 17:56–69CrossRef
Zurück zum Zitat Grilli L, Iannario M, Piccolo D, Rampichini C (2014) Latent class CUB models. Adv Data Anal Classif 8:105–119MathSciNetCrossRef Grilli L, Iannario M, Piccolo D, Rampichini C (2014) Latent class CUB models. Adv Data Anal Classif 8:105–119MathSciNetCrossRef
Zurück zum Zitat Iannario M (2007) A statistical approach for modelling urban audit perception surveys. Quaderni di Statistica 9:149–172 Iannario M (2007) A statistical approach for modelling urban audit perception surveys. Quaderni di Statistica 9:149–172
Zurück zum Zitat Iannario M (2009) Fitting measures for ordinal data models. Quaderni di Statistica 11:39–72 Iannario M (2009) Fitting measures for ordinal data models. Quaderni di Statistica 11:39–72
Zurück zum Zitat Iannario M (2015) Detecting latent components in ordinal data with overdispersion by means of a mixture distribution. Qual Quant 49(3):977–987MathSciNetCrossRef Iannario M (2015) Detecting latent components in ordinal data with overdispersion by means of a mixture distribution. Qual Quant 49(3):977–987MathSciNetCrossRef
Zurück zum Zitat Iannario M, Piccolo D (2010) A new statistical model for the analysis of customer satisfaction. Qual Technol Quant Manag 7:149–168CrossRef Iannario M, Piccolo D (2010) A new statistical model for the analysis of customer satisfaction. Qual Technol Quant Manag 7:149–168CrossRef
Zurück zum Zitat Iannario M, Piccolo D (2012a) CUB models: statistical methods and empirical evidence. In: Kenett R, Salini S (eds) Modern analysis of customer surveys: with applications using R. Wiley, Chichester, pp 231–258 Iannario M, Piccolo D (2012a) CUB models: statistical methods and empirical evidence. In: Kenett R, Salini S (eds) Modern analysis of customer surveys: with applications using R. Wiley, Chichester, pp 231–258
Zurück zum Zitat Iannario M, Piccolo D (2012b) A framework for modelling ordinal data in rating surveys. Proc Jt Stat Meet Market Res Sect 7:1–15 Iannario M, Piccolo D (2012b) A framework for modelling ordinal data in rating surveys. Proc Jt Stat Meet Market Res Sect 7:1–15
Zurück zum Zitat Iannario M, Piccolo D (2014) Inference for CUB models: a program in R. Stat & Appl. XII:177–204 Iannario M, Piccolo D (2014) Inference for CUB models: a program in R. Stat & Appl. XII:177–204
Zurück zum Zitat Kokonendji C, Zocchi S (2010) Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions. Stat Probab Lett 80:1655–1662MathSciNetCrossRefMATH Kokonendji C, Zocchi S (2010) Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions. Stat Probab Lett 80:1655–1662MathSciNetCrossRefMATH
Zurück zum Zitat Kulas J, Stachowski A (2009) Middle category endorsement in odd-numbered Likert response scales: associated item characteristics, cognitive demands, and preferred meanings. J Res Pers 43(3):489–493CrossRef Kulas J, Stachowski A (2009) Middle category endorsement in odd-numbered Likert response scales: associated item characteristics, cognitive demands, and preferred meanings. J Res Pers 43(3):489–493CrossRef
Zurück zum Zitat Lentz T (1938) Acquiescence as a factor in the measurement of personality. Psychol Bull 35:659 Lentz T (1938) Acquiescence as a factor in the measurement of personality. Psychol Bull 35:659
Zurück zum Zitat McLachlan G, Krishnan T (2008) The EM algorithm and extensions, 2nd edn. Wiley, New YorkCrossRefMATH McLachlan G, Krishnan T (2008) The EM algorithm and extensions, 2nd edn. Wiley, New YorkCrossRefMATH
Zurück zum Zitat Moors G (2008) Exploring the effect of a middle response category on response style in attitude measurement. Qual Quant 42:779–794CrossRef Moors G (2008) Exploring the effect of a middle response category on response style in attitude measurement. Qual Quant 42:779–794CrossRef
Zurück zum Zitat Pesaran M, Ulloa M (2008) Non-nested hypotheses. In: Durlauf ESN, Blume LE (eds) The new palgrave: a dictionary of economics, , vol 6, 2nd edn, pp 107–114 Pesaran M, Ulloa M (2008) Non-nested hypotheses. In: Durlauf ESN, Blume LE (eds) The new palgrave: a dictionary of economics, , vol 6, 2nd edn, pp 107–114
Zurück zum Zitat Piccolo D (2003) On the moments of a mixture of uniform and shifted binomial random variables. Quaderni di Statistica 5:86–104 Piccolo D (2003) On the moments of a mixture of uniform and shifted binomial random variables. Quaderni di Statistica 5:86–104
Zurück zum Zitat Piccolo D (2006) Observed information matrix for MUB models. Quaderni di Statistica 8:33–78 Piccolo D (2006) Observed information matrix for MUB models. Quaderni di Statistica 8:33–78
Zurück zum Zitat Poulton E (1989) Bias in quantifying judgements. Psychology Press, Hillsdale Poulton E (1989) Bias in quantifying judgements. Psychology Press, Hillsdale
Zurück zum Zitat Simon H (1957) Models of man; social and rational. Wiley, New YorkMATH Simon H (1957) Models of man; social and rational. Wiley, New YorkMATH
Zurück zum Zitat Tutz G (2012) Regression for categorical data. Cambridge University Press, CambridgeMATH Tutz G (2012) Regression for categorical data. Cambridge University Press, CambridgeMATH
Metadaten
Titel
Varying uncertainty in CUB models
verfasst von
Anna Gottard
Maria Iannario
Domenico Piccolo
Publikationsdatum
01.06.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Advances in Data Analysis and Classification / Ausgabe 2/2016
Print ISSN: 1862-5347
Elektronische ISSN: 1862-5355
DOI
https://doi.org/10.1007/s11634-016-0235-0

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