Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects

Sophia Rabe-Hesketh, Anders Skrondal, Andrew Pickles

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Gauss-Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables. The models can include several nested random effects (intercepts and coefficients) representing unobserved heterogeneity at different levels of a hierarchical dataset. The required multivariate integrals are evaluated efficiently using spherical quadrature rules. Simulations show that adaptive quadrature performs well in a wide range of situations. © 2004 Published by Elsevier B.V.
    Original languageEnglish
    Pages (from-to)301-323
    Number of pages22
    JournalJournal of Econometrics
    Volume128
    Issue number2
    DOIs
    Publication statusPublished - Oct 2005

    Keywords

    • Adaptive quadrature
    • GLLAMM
    • Hierarchical models
    • Multilevel models
    • Numerical integration
    • Random coefficients
    • Random effects
    • Spherical quadrature rules

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