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Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores

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  • D. R. Cox
  • Nanny Wermuth

Abstract

After some discussion of the purposes of testing multivariate normality, the paper concentrates on two different approaches to testing linearity: on repeated regression tests of nonlinearity and on exploiting properties of a dichotomized normal distribution. Regression tests of linearity are used to examine the adequacy of linear scoring systems for explanatory variables, initially recorded on an ordinal scale. Examples from recent psychological and medical research are given in which the methods have led to some insight into subject‐matter.

Suggested Citation

  • D. R. Cox & Nanny Wermuth, 1994. "Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 347-355, June.
    • Handle: RePEc:bla:jorssc:v:43:y:1994:i:2:p:347-355
    DOI: 10.2307/2986025
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    Cited by:

    1. Foraita, Ronja & Klasen, Stephan & Pigeot, Iris, 2008. "Using graphical chain models to analyze differences in structural correlates of undernutrition in Benin and Bangladesh," Economics & Human Biology, Elsevier, vol. 6(3), pages 398-419, December.
    2. Kristian Hindberg & Jan Hannig & Fred Godtliebsen, 2019. "A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-20, January.
    3. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    4. Riccardo LUCCHETTI & Claudia PIGINI, 2011. "Conditional Moment Tests for Normality in Bivariate Limited Dependent Variable Models: a Monte Carlo Study," Working Papers 357, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    5. Bogdan, Malgorzata, 1999. "Data Driven Smooth Tests for Bivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 26-53, January.
    6. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    7. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    8. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    9. Ttofi, Maria M. & Farrington, David P. & Piquero, Alex R. & Lösel, Friedrich & DeLisi, Matthew & Murray, Joseph, 2016. "Intelligence as a protective factor against offending: A meta-analytic review of prospective longitudinal studies," Journal of Criminal Justice, Elsevier, vol. 45(C), pages 4-18.

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