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Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation

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Author Info

  • Lorenzo Cappellari

    () (Catholic University of Milan, University of Essex)

  • Stephen P. Jenkins

    () (University of Essex)

Abstract

We discuss methods for calculating multivariate normal probabilities by simulation and two new Stata programs for this purpose: mdraws for deriving draws from the standard uniform density using either Halton or pseudorandom sequences, and an egen function, mvnp(), for calculating the probabilities them- selves. Several illustrations show how the programs may be used for maximum simulated likelihood estimation. Copyright 2006 by StataCorp LP.

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Bibliographic Info

Article provided by StataCorp LP in its journal Stata Journal.

Volume (Year): 6 (2006)
Issue (Month): 2 (June)
Pages: 156-189

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Handle: RePEc:tsj:stataj:v:6:y:2006:i:2:p:156-189

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Related research

Keywords: mdraws; egen function mvnp( ); simulation estimation; maxi- mum simulated likelihood; multivariate probit; Halton sequences; pseudorandom sequences; multivariate normal; GHK simulator;

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References

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  1. repec:ese:iserwp:2002-08 is not listed on IDEAS
  2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
  3. Stephane Hess & John Polak, 2003. "An alternative method to the scrambled Halton sequence for removing correlation between standard Halton sequences in high dimensions," ERSA conference papers ersa03p406, European Regional Science Association.
  4. William W. Gould & Jeffrey Pitblado & Brian Poi, 2010. "Maximum Likelihood Estimation with Stata," Stata Press books, StataCorp LP, edition 4, number ml4, February.
  5. Peter Haan & Arne Uhlendorff, 2006. "Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 6(2), pages 229-245, June.
  6. repec:ese:iserwp:2004-27 is not listed on IDEAS
  7. Lorenzo Cappellari & Stephen P. Jenkins, 2002. "Modelling Low Income Transitions," Discussion Papers of DIW Berlin 288, DIW Berlin, German Institute for Economic Research.
  8. Stephen P. Jenkins & Lorenzo Cappellari & Peter Lynn & Annette Jäckle & Emanuela Sala, 2006. "Patterns of consent: evidence from a general household survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 701-722.
  9. Sandor, Zsolt & Andras, P.Peter, 2004. "Alternative sampling methods for estimating multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 120(2), pages 207-234, June.
  10. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," United Kingdom Stata Users' Group Meetings 2003 10, Stata Users Group.
  11. Mark Stewart, 2006. "Maximum simulated likelihood estimation of random-effects dynamic probit models with autocorrelated errors," Stata Journal, StataCorp LP, vol. 6(2), pages 256-272, June.
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