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The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates

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  • Opeyo Peter Otieno

    (Department of Statistics, Beijing University of Technology, Beijing 100124, China
    Department of Statistics and Computational Mathematics, The Technical University of Kenya, Nairobi P.O. Box 52428-00200, Kenya)

  • Weihu Cheng

    (Department of Statistics, Beijing University of Technology, Beijing 100124, China)

Abstract

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton–Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models.

Suggested Citation

  • Opeyo Peter Otieno & Weihu Cheng, 2023. "The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4338-:d:1262590
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    References listed on IDEAS

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    2. Fang, Fang & Shao, Jun, 2016. "Iterated imputation estimation for generalized linear models with missing response and covariate values," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 111-123.
    3. William Greene, 2004. "The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 98-119, June.
    4. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    5. Matyas, Laszlo & Lovrics, Laszlo, 1991. "Missing observations and panel data : A Monte-Carlo analysis," Economics Letters, Elsevier, vol. 37(1), pages 39-44, September.
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