Otieno, O.P.; Cheng, W. The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates. Mathematics2023, 11, 4338.
Otieno, O.P.; Cheng, W. The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates. Mathematics 2023, 11, 4338.
Otieno, O.P.; Cheng, W. The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates. Mathematics2023, 11, 4338.
Otieno, O.P.; Cheng, W. The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates. Mathematics 2023, 11, 4338.
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 the parameters have been conducted for cases of complete data sets and also longitudinal models. For binary response fixed effects panel data model, the conditional logit estimator is consistent for balanced data. When faced with missing covariates problem, researchers opt for various imputation techniques to make the data complete 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 which yields the best estimates with minimum variance is still elusive. The main aim of this paper is to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector which will make the Newton-Raphson algorithm to 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 partitioning of the covariate matrix. We also confirm from the moduli of the Hessian matrices that the log likelihood of a panel data logistic model has a global maximum as the parameter estimates. Simulation results reveal that model based simulation perform better than classical imputation techniques yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models with single fixed effects.
Keywords
Maximum Likelihood; Fixed effects; Conditional logit; Hessian matrix
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
