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Obtaining reliable likelihood ratio tests from simulated likelihood functions.

Laura Mørch Andersen1

  • 1Department of Food and Resource Economics, University of Copenhagen, Frederiksberg, Copenhagen, Denmark.

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Asymmetric draws in mixed models can lead to inconsistent likelihood ratio tests. Fully antithetic draws, not just one-dimensionally, are essential for accurate statistical testing in mixed models.

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Mixed models with continuous heterogeneity are increasingly popular.
  • Current standard practice uses asymmetric draws (e.g., Halton draws) for simulations in mixed models.
  • This practice is the default in many statistical programs.

Purpose of the Study:

  • To identify inconsistencies in likelihood ratio (LR) tests caused by asymmetric draws in mixed models.
  • To propose a solution for maintaining correct dimensions when reducing the mixing distribution in these models.

Main Methods:

  • The study analyzes the impact of standard deviations of mixed parameters on LR test statistics.
  • It demonstrates the inefficiency of increasing draw numbers to correct for asymmetric draw issues.
  • The research proposes using fully antithetic draws and replicating relevant dimensions in restricted likelihood simulations.

Main Results:

  • Asymmetric draws frequently lead to misleading LR test results, especially when likelihood functions depend on standard deviations.
  • Increasing the number of draws is an inefficient strategy to ensure test statistic accuracy.
  • Fully antithetic draws completely solve the problem of inconsistent LR tests, while one-dimensionally antithetic draws are insufficient.

Conclusions:

  • Fully antithetic draws are necessary for accurate LR tests in mixed models with continuous heterogeneity.
  • Models reducing mixing distribution dimensions must replicate relevant quasi-random draw dimensions during restricted likelihood simulation.
  • The study recommends adopting fully antithetic draws and dimension replication as default options in statistical software.