Abstract
Stochastic simulation is a significant aspect of statistical research. Model building, parameter estimation, hypothesis tests, and other statistical tools for data analysis require verification to assess their validity and reliability, typically via simulated data. In many research fields, data sets often include ordinal variables, e.g. measured on a Likert scale, or count variables. In this work, we present and discuss a simulation method for generating ordinal and discrete random variables, whose marginal distributions and correlation matrix (expressed in terms of Pearson or Spearman’s pairwise correlations) are assigned by the user.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barbiero, A., Ferrari, P.A.: GenOrd: Simulation of ordinal and discrete variables with given correlation matrix and marginal distributions. R package version 1.2.0. http://CRAN.R-project.org/package=GenOrd (2014)
Bonett, D.G., Wright, T.A.: Sample size requirements for estimating Pearson, Kendall and Spearman correlations. Psychometrika 1, 23–28 (2000)
Bracquemond, C., Crétois, E., Gaudoin, O.: A comparative study of goodness-of-fit tests for the geometric distribution and application to discrete time reliability, Technical Report, http://www-ljk.imag.fr/SMS/ftp/BraCreGau02.pdf (2002)
Cario, M.C., Nelson, B.L.: Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston (1997)
Demirtas, H.: A method for multivariate ordinal data generation given marginal distributions and correlations. J. Stat. Comput. Simul. 76(11), 1017–1025 (2006)
Ferrari, P.A., Barbiero, A.: Simulating ordinal data. Multivariate Behav. Res. 47(4), 566–589 (2012)
Guilford, J.P.: Fundamental Statistics in Psychology and Education. McGraw-Hill, New York (1965)
Kocherlakota, S., Kocherlakota, K.: Goodness-of-fit tests for discrete distributions. Commun. Stat. Theory Methods 15, 815–829 (1986)
Pearson, K.: Mathematical contributions to the theory of evolution: XVI. On further methods of determining correlation. In: Draper’s Research Memoirs. Biometric Series, vol. 4. Cambridge University Press, Cambridge (1907)
Ruscio, J., Kaczetow, W.: Simulating multivariate nonnormal data using an iterative algorithm. Multivariate Behav. Res. 3, 355–381 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this paper
Cite this paper
Barbiero, A., Ferrari, P.A. (2014). Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_4
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2104-1_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2103-4
Online ISBN: 978-1-4939-2104-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)