Skip to main content
SpringerLink
Log in

Pairwise likelihood estimation for the normal ogive model with binary data

  • Original Paper
  • Published:
AStA Advances in Statistical Analysis Aims and scope Submit manuscript

Abstract

A marginal pairwise likelihood estimation approach is examined in the normal ogive model with binary response. This method, belonging to the broad class of composite likelihood, provides estimators with desirable asymptotic properties such as consistency and asymptotic normality. We study the performance of the proposed methodology by a simulation and we compare it with marginal maximum likelihood. The different results are also illustrated with an analysis of a real data set from a quality of life study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Albert, J.H.: Bayesian estimation of normal ogive item response curves using Gibbs sampling. J. Educ. Stat. 17, 251–269 (1992)

    Article  Google Scholar 

  • Baker, F.B., Kim, S.H.: Item Response Theory. Parameter Estimation Techniques. Marcel Dekker, New York (2004)

    MATH  Google Scholar 

  • Bellio, R., Varin, C.: A pairwise likelihood approach to generalized linear models with crossed effects. Stat. Model. 5, 217–227 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Bergner, M., et al.: The sickness impact profile: validation of a health status measure. Med. Care 14, 56–67 (1973)

    Google Scholar 

  • Besag, J.E.: Statistical analysis of non lattice data. Statistician 24(2), 179–195 (1975)

    Article  Google Scholar 

  • Birnbaum, A.: Some latent trait models and their use in inferring an examinees ability. In: Lord, F.M., Novick, M.R. (eds.) Statistical Theories of Mental Test Scores, pp. 395–479. Addison Wesley, Massachusetts (1960)

    Google Scholar 

  • Cox, D.R., Reid, N.: A note on pseudolikelihood constructed from marginal densities. Biometrika 91, 729–737 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Fechner, G.T.: Elemente der Psychophysik. Breitkopf und Hartel, Leipzig (1960)

    Google Scholar 

  • Feddag, M.L., Grama, I., Mesbah, M.: Generalized estimating equations for mixed logistic models. Commun. Stat.: Theory Methods 32(4), 851–874 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Feddag, M.L., Bacci, S.: Pairwise likelihood for the longitudinal mixed Rasch model. Comput. Stat. Data Anal. 53, 1027–1037 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Ferguson, G.A.: Item selection by the constant process. Psychometrika 7, 19–29 (1942)

    Article  Google Scholar 

  • Finney, D.J.: The application of probit analysis to the results on mental tests. Psychometrika 19, 31–39 (1944)

    Article  Google Scholar 

  • Fischer, G.H., Molenaar, I.W.: Rasch Models Foundations. Recents Developments and Applications. Springer-Verlag, Berlin (1995)

    Google Scholar 

  • Kang, W., Lee, M.S., Lee, Y.: HGLM versus conditional estimators for the analysis of clustered binary data. Stat. Med. 24, 741–752 (2005)

    Article  MathSciNet  Google Scholar 

  • Kuk, Y.C., Nott, D.N.: A pairwise likelihood approach to analyzing correlated binary data. Stat. Probab. Lett. 47, 329–335 (2000)

    Article  MATH  Google Scholar 

  • LeCessie, S., van Houwelingen, J.C.: Logistic regression for correlated binary data. Appl. Stat. 43, 95–108 (1994)

    Article  MATH  Google Scholar 

  • Lindsay, B.G.: Composite likelihood methods. In: Prablu, N.U. (ed.) Statistical Inference from Stochastic Processes Comtemporary Mathematics, vol. 80, pp. 221–239. American Mathematical Society, Providence (1988)

    Chapter  Google Scholar 

  • Lord, F.M.: A theory of test scores. Psychometric Monograph, No. 7 (1952)

  • Lord, F.M., Novick, M.R.: Statistical Theories of Mental Test Scores. Addison-Wesley Publishing Company, Reading (1968)

    MATH  Google Scholar 

  • Muller, G.E.: Die Gesichtspunkte und die Tatsachen der psychophysischen Methodik. Bergmann, Wiesbaden (1904)

    Google Scholar 

  • R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.ISBN (2005)

  • Renard, D., Geert, G., Geys, H.: A pairwise likelihood approach to estimation in multilevel probit models. Comput. Stat. Data Anal. 44, 649–667 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Richardson, M.W.: The relationship between difficulty and the differential validity of a test. Psychometrika 1(2), 33–49 (1936)

    Article  MATH  Google Scholar 

  • Rigdon, S.E., Tsutakawa, R.K.: Parameter estimation in latent trait models. Psychometrika 48, 567–574 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  • STATA base reference manual G-M release: A Stata Press Publication. STATA Corporation, College Station, Texas (2003)

  • Thomson, G.H.: A direct deduction of the constant process used in the method of right and wrong cases. Psychol. Rev. 26, 454–464 (1919)

    Article  Google Scholar 

  • Urban, F.M.: Die psychophysischen Massmethoden als Grundlagen empirisher Messungen. Archiv fur die gesamte Psychologie 15, 261–355 (1910a)

  • Urban, F.M.: Die psychophysischen Massmethoden als Grundlagen empirisher Messungen. Archiv fur die gesamte Psychologie 16, 168–227 (1910b)

  • van der Linden, W.J., Hambleton, R.K.: Handbook of Modern Item response Theory. Springer-Verlag, New York (1997)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EA 4275 “Biostatistique, Recherche Clinique et Mesures Subjectives en Sante”, Faculté de Pharmacie, Université de Nantes, 1 rue Gaston Veil, 44035, Nantes, France

    M.-L. Feddag

Authors
  1. M.-L. Feddag
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M.-L. Feddag.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feddag, ML. Pairwise likelihood estimation for the normal ogive model with binary data. AStA Adv Stat Anal 100, 223–237 (2016). https://doi.org/10.1007/s10182-015-0263-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10182-015-0263-7

Keywords

Search

Navigation