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A new Stata command for estimating confidence intervals for the variance component of random-effects linear models

Author

Listed:
  • Matteo Bottai

    (Arnold School of Public Health, University of South Carolina, Columbia, SC
    Institute of Information Science and Technology, National Research Council, Pisa)

  • Nicola Orsini

    (Institute of Information Science and Technology, National Research Council, Pisa
    Institute of Environmental Medicine, Karolinska Institutet, Stockholm)

Abstract

The Stata command xtreg estimates the random-effects linear regression model, for which the random effects are assumed to be normally distributed with zero mean and non-negative variance, s^2_{i,t}. Testing homogeneity across units is equivalent to testing the null hypothesis H_0: s^2_{i,t} = 0, which is a value on the boundary of the parameter space. The command xtreg provides the upper-tail probability of the appropriate asymptotic distribution of the likelihood ratio test statistic. However, such a method cannot be used to construct confidence intervals for the parameter s^2_{i,t}. Besides, confidence intervals for the random-effect variance that are based on a Wald-type test, too often used, can be shown to be asymptotically wrong. Based on the asymptotic theory for singular information problems, a method is developed and implemented in the Stata command xtci, which provides asymptotically-correct confidence intervals. Also, when testing the hypothesis of homogeneity across units, the proposed method is shown to have better small-sample properties than one based on the likelihood ratio test statistic.

Suggested Citation

  • Matteo Bottai & Nicola Orsini, 2004. "A new Stata command for estimating confidence intervals for the variance component of random-effects linear models," United Kingdom Stata Users' Group Meetings 2004 5, Stata Users Group.
    • Handle: RePEc:boc:usug04:5
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