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Alternative Simulation-Based Estimators of Logit Models with Random Effects

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Abstract

Logit models with random effects are now widely used in applied Statistics and Econometrics. They usually lead to intractable likelihood functions, as they involve integrals without closed form solution. Numerical integration can be used to compute the likelihood and software is available (Hedeker and Gibbons, 1996). Difficulties can be encountered when the number of random effect parameters is not very small. With a detailed Monte Carlo experimentation, we show in this paper that the simulation-based estimators are almost as efficient as maximum likelihood. They are Simulated Maximum Likelihood (Gouri´eroux and Monfort, 1991), Indirect Inference (Gouri´eroux, Monfort and Renault, 1993) using an auxiliary approximated likelihood estimator, and Indirect Inference using an auxiliary linear probability model. The advantage of the latter is its great simplicity and computational speed.

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  • Giorgio Calzolari & F. Mealli & C. Rampichini, 2001. "Alternative Simulation-Based Estimators of Logit Models with Random Effects," Econometrics Working Papers Archive quaderno48, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  • Handle: RePEc:fir:econom:quaderno48
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    References listed on IDEAS

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    1. Giorgio Calzolari & Francesca Di Iorio & Gabriele Fiorentini, 1998. "Control variates for variance reduction in indirect inference: Interest rate models in continuous time," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 100-112.
    2. Stephen Pudney & Michael Shields, 2000. "Gender, race, pay and promotion in the British nursing profession: estimation of a generalized ordered probit model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(4), pages 367-399.
    3. Mealli, Fabrizia & Pudney, Stephen, 1996. "Occupational Pensions and Job Mobility in Britain: Estimation of a Random-Effects Competing Risks Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 293-320, May-June.
    4. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    5. Bianchi, Carlo & Calzolari, Giorgio & Corsi, Paolo, 1978. "A Program for Stochastic Simulation of Econometric Models," Econometrica, Econometric Society, vol. 46(1), pages 235-236, January.
    6. Longford, N. T., 1994. "Logistic regression with random coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 17(1), pages 1-15, January.
    7. Mealli, Fabrizia & Rampichini, Carla, 1999. "Estimating binary multilevel models through indirect inference," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 313-324, January.
    8. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 945-973.
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    Cited by:

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    2. Anna Gottard & Giorgio Calzolari, 2014. "Alternative estimating procedures for multiple membership logit models with mixed effects: indirect inference and data cloning," Econometrics Working Papers Archive 2014_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".

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