Skip to main content

2015 | OriginalPaper | Buchkapitel

5. Categorical Data

verfasst von : Peter Müller, Fernando Andrés Quintana, Alejandro Jara, Tim Hanson

Erschienen in: Bayesian Nonparametric Data Analysis

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We discuss nonparametric Bayesian methods that are suitable for inference with binary, ordinal and general categorical data. Modeling for such data becomes particularly interesting in the presence of covariates, when non- and semi-parametric Bayesian models can generalize the link function in a generalized linear model setup, the regression on covariates or both. An important application arises in inference for diagnostic screening and related inference for ROC (receiver-operator characteristic) curves. We include some discussion of a rapidly growing literature on non-parametric Bayesian inference for ROC curves.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Albright SC (1993) A statistical analysis of hitting streaks in baseball. J Am Stat Assoc 88:1175–1183CrossRef Albright SC (1993) A statistical analysis of hitting streaks in baseball. J Am Stat Assoc 88:1175–1183CrossRef
Zurück zum Zitat Bao J, Hanson T (2015) Bayesian nonparametric multivariate ordinal regression. Can J Stat (in press) Bao J, Hanson T (2015) Bayesian nonparametric multivariate ordinal regression. Can J Stat (in press)
Zurück zum Zitat Bishop YMM, Fienberg SE, Holland PW (1975) Discrete multivariate analyses: theory and practice. MIT Press, CambridgeMATH Bishop YMM, Fienberg SE, Holland PW (1975) Discrete multivariate analyses: theory and practice. MIT Press, CambridgeMATH
Zurück zum Zitat Branscum A, Johnson W, Hanson T, Gardner I (2008) Bayesian semiparametric ROC curve estimation and disease risk assessment. Stat Med 27:2474–2496MathSciNetCrossRef Branscum A, Johnson W, Hanson T, Gardner I (2008) Bayesian semiparametric ROC curve estimation and disease risk assessment. Stat Med 27:2474–2496MathSciNetCrossRef
Zurück zum Zitat Breslow NE, Clayton D (1993) Approximate inference in generealized linear models. J Am Stat Assoc 88:9–25MATH Breslow NE, Clayton D (1993) Approximate inference in generealized linear models. J Am Stat Assoc 88:9–25MATH
Zurück zum Zitat de Carvalho V, Jara A, Hanson T, de Carvalho M (2013) Bayesian nonparametric ROC regression modeling. Bayesian Anal 8:623–646MathSciNetCrossRef de Carvalho V, Jara A, Hanson T, de Carvalho M (2013) Bayesian nonparametric ROC regression modeling. Bayesian Anal 8:623–646MathSciNetCrossRef
Zurück zum Zitat Diaconis P, Ylvisaker D (1985) Quantifying prior opinion. In: Bayesian statistics, vol 2 (Valencia, 1983). North-Holland, Amsterdam, pp 133–156 (with discussion and a reply by Diaconis) Diaconis P, Ylvisaker D (1985) Quantifying prior opinion. In: Bayesian statistics, vol 2 (Valencia, 1983). North-Holland, Amsterdam, pp 133–156 (with discussion and a reply by Diaconis)
Zurück zum Zitat Diggle PJ, Liang KY, Zeger SL (1994) Analysis of longitudinal data. Oxford University Press, Oxford Diggle PJ, Liang KY, Zeger SL (1994) Analysis of longitudinal data. Oxford University Press, Oxford
Zurück zum Zitat Gross P (1971) A study of supervisor reliability. Mimeograph, Laboratory of Human Development. Harvard Graduate School of Education, Cambridge Gross P (1971) A study of supervisor reliability. Mimeograph, Laboratory of Human Development. Harvard Graduate School of Education, Cambridge
Zurück zum Zitat Hanson T, Kottas A, Branscum A (2008) Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian nonparametric approaches. J R Stat Soc Ser C 57:207–225MATHMathSciNetCrossRef Hanson T, Kottas A, Branscum A (2008) Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian nonparametric approaches. J R Stat Soc Ser C 57:207–225MATHMathSciNetCrossRef
Zurück zum Zitat Hjort NL, Ongaro A (2005) Exact inference for random Dirichlet means. Stat Infer Stoch Process (An International Journal Devoted to Time Series Analysis and the Statistics of Continuous Time Processes and Dynamical Systems) 8(3):227–254MATHMathSciNet Hjort NL, Ongaro A (2005) Exact inference for random Dirichlet means. Stat Infer Stoch Process (An International Journal Devoted to Time Series Analysis and the Statistics of Continuous Time Processes and Dynamical Systems) 8(3):227–254MATHMathSciNet
Zurück zum Zitat Jara A, García-Zattera MJ, Lesaffre E (2006) Semiparametric Bayesian analysis of misclassified binary data. In: XXIII international biometric conference, July 16–21, Montréal, Canada Jara A, García-Zattera MJ, Lesaffre E (2006) Semiparametric Bayesian analysis of misclassified binary data. In: XXIII international biometric conference, July 16–21, Montréal, Canada
Zurück zum Zitat Jara A, García-Zattera MJ, Lesaffre E (2007) A Dirichlet process mixture model for the analysis of correlated binary responses. Comput Stat Data Anal 51:5402–5415MATHCrossRef Jara A, García-Zattera MJ, Lesaffre E (2007) A Dirichlet process mixture model for the analysis of correlated binary responses. Comput Stat Data Anal 51:5402–5415MATHCrossRef
Zurück zum Zitat Jara A, Hanson T, Lesaffre E (2009) Robustifying generalized linear mixed models using a new class of mixture of multivariate Polya trees. J Comput Graph Stat 18:838–860MathSciNetCrossRef Jara A, Hanson T, Lesaffre E (2009) Robustifying generalized linear mixed models using a new class of mixture of multivariate Polya trees. J Comput Graph Stat 18:838–860MathSciNetCrossRef
Zurück zum Zitat Johnson VE, Albert JH (1999) Ordinal data modeling. Springer, New YorkMATH Johnson VE, Albert JH (1999) Ordinal data modeling. Springer, New YorkMATH
Zurück zum Zitat Kleinman KP, Ibrahim JG (1998) A semi-parametric Bayesian approach to generalized linear mixed models. Stat Med 17:2579–2596CrossRef Kleinman KP, Ibrahim JG (1998) A semi-parametric Bayesian approach to generalized linear mixed models. Stat Med 17:2579–2596CrossRef
Zurück zum Zitat Kottas A, Müller P, Quintana FA (2005) Nonparametric Bayesian modeling for multivariate ordinal data. J Comput Graph Stat 14:610–625CrossRef Kottas A, Müller P, Quintana FA (2005) Nonparametric Bayesian modeling for multivariate ordinal data. J Comput Graph Stat 14:610–625CrossRef
Zurück zum Zitat Kraemer HC (1992) Evaluating medical tests. Sage Publications, Newbury Park Kraemer HC (1992) Evaluating medical tests. Sage Publications, Newbury Park
Zurück zum Zitat Li Y, Müller P, Lin X (2011) Center-adjusted inference for a nonparametric Bayesian random effect distribution. Stat Sin 21(3):1201–1223MATHCrossRef Li Y, Müller P, Lin X (2011) Center-adjusted inference for a nonparametric Bayesian random effect distribution. Stat Sin 21(3):1201–1223MATHCrossRef
Zurück zum Zitat Liu JS (1996) Nonparametric hierarchical Bayes via sequential imputations. Ann Stat 24:911–930MATHCrossRef Liu JS (1996) Nonparametric hierarchical Bayes via sequential imputations. Ann Stat 24:911–930MATHCrossRef
Zurück zum Zitat Lunn D, Spiegelhalter D, Thomas A, Best N (2009) The BUGS project: Evolution, critique and future directions (Pkg: P3049–3082). Stat Med 28(25):3049–3067MathSciNetCrossRef Lunn D, Spiegelhalter D, Thomas A, Best N (2009) The BUGS project: Evolution, critique and future directions (Pkg: P3049–3082). Stat Med 28(25):3049–3067MathSciNetCrossRef
Zurück zum Zitat McCullagh P, Nelder JA (1983) Generalized linear models. Monographs on statistics and applied probability. Chapman & Hall, LondonCrossRef McCullagh P, Nelder JA (1983) Generalized linear models. Monographs on statistics and applied probability. Chapman & Hall, LondonCrossRef
Zurück zum Zitat McMillan G, Hanson T, Bedrick E, Lapham S (2005) Using the bivariate Dale model to jointly estimate predictors of frequency and quantity of alcohol use. J Stud Alcohol 65:643–650 McMillan G, Hanson T, Bedrick E, Lapham S (2005) Using the bivariate Dale model to jointly estimate predictors of frequency and quantity of alcohol use. J Stud Alcohol 65:643–650
Zurück zum Zitat Morton AQ (1978) Literary detection. Scribner’s, New York Morton AQ (1978) Literary detection. Scribner’s, New York
Zurück zum Zitat Müller P, Rosner G (1997) A Bayesian population model with hierarchical mixture priors applied to blood count data. J Am Stat Assoc 92:1279–1292MATH Müller P, Rosner G (1997) A Bayesian population model with hierarchical mixture priors applied to blood count data. J Am Stat Assoc 92:1279–1292MATH
Zurück zum Zitat Newton MA, Czado C, Chapell R (1996) Bayesian inference for semiparametric binary regression. J Am Stat Assoc 91:142–153MATHCrossRef Newton MA, Czado C, Chapell R (1996) Bayesian inference for semiparametric binary regression. J Am Stat Assoc 91:142–153MATHCrossRef
Zurück zum Zitat Quintana FA (1998) Nonparametric Bayesian analysis for assessing homogeneity in k × l contingency tables with fixed right margin totals. J Am Stat Assoc 93:1140–1149MATHMathSciNet Quintana FA (1998) Nonparametric Bayesian analysis for assessing homogeneity in k × l contingency tables with fixed right margin totals. J Am Stat Assoc 93:1140–1149MATHMathSciNet
Zurück zum Zitat Rice JA (1995) Mathematical statistics and data analysis, 2nd edn. Duxbury Press, BelmontMATH Rice JA (1995) Mathematical statistics and data analysis, 2nd edn. Duxbury Press, BelmontMATH
Zurück zum Zitat Tutz G (2012) Regression for categorical data. Cambridge series in statistical and probabilistic mathematics, vol 34. Cambridge University Press, Cambridge Tutz G (2012) Regression for categorical data. Cambridge series in statistical and probabilistic mathematics, vol 34. Cambridge University Press, Cambridge
Zurück zum Zitat Zeger SL, Karim MR (1991) Generalized linear models with random effects: a Gibbs sampling approach. J Am Stat Assoc 86:79–86MathSciNetCrossRef Zeger SL, Karim MR (1991) Generalized linear models with random effects: a Gibbs sampling approach. J Am Stat Assoc 86:79–86MathSciNetCrossRef
Metadaten
Titel
Categorical Data
verfasst von
Peter Müller
Fernando Andrés Quintana
Alejandro Jara
Tim Hanson
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-18968-0_5