This paper develops a Lambert-Topp-Leone (LTL) regression model for limited responses and explores the use of classical and metaheuristic optimisation strategies for maximum likelihood estimation. Grey Wolf Optimiser (GWO) and Differential Evolution (DE) are compared with BFGS and Nelder-Mead using Monte Carlo simulations with different parameter configurations and sample sizes. The performance is evaluated based on bias, RMSE, likelihood achievement, convergence dependability, and computing time. The results show that BFGS performs well under normal likelihood setups, while GWO and DE become competitive under more challenging parameter choices, showing that neither optimiser is uniformly superior.. An application to the MockJurors data indicates that the four techniques yield roughly the same LTL maximum likelihood solutions, lending support to the employment of metaheuristic algorithms as complementary global-search tools for assessing the numerical stability of LTL regression estimates.
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