This chapter serves as a practical programming guide to implementing maximum likelihood estimation (MLE) in Stata. It begins by elucidating the foundational statistical principles of MLE, providing the theoretical context necessary for custom model development. The focus then shifts to practical application, introducing Stata’s powerful ml module as the primary tool for user-defined estimations. To solidify understanding, the chapter presents a detailed, step-by-step case study: the Maximum Likelihood estimation of a standard linear regression model. This comprehensive example demonstrates two distinct programming approaches. First, it illustrates how to construct a complete Stata ado command for the estimation. Second, it details how to program the corresponding log-likelihood function efficiently using Stata's matrix programming language, Mata. By walking through this end-to-end example, this guide equips readers with the essential skills to program and fit their own custom statistical models using the flexible MLE framework within Stata.

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A Programming Guide to Maximum Likelihood Estimation in Stata

  • Ning Zhang,
  • Kerui Du

摘要

This chapter serves as a practical programming guide to implementing maximum likelihood estimation (MLE) in Stata. It begins by elucidating the foundational statistical principles of MLE, providing the theoretical context necessary for custom model development. The focus then shifts to practical application, introducing Stata’s powerful ml module as the primary tool for user-defined estimations. To solidify understanding, the chapter presents a detailed, step-by-step case study: the Maximum Likelihood estimation of a standard linear regression model. This comprehensive example demonstrates two distinct programming approaches. First, it illustrates how to construct a complete Stata ado command for the estimation. Second, it details how to program the corresponding log-likelihood function efficiently using Stata's matrix programming language, Mata. By walking through this end-to-end example, this guide equips readers with the essential skills to program and fit their own custom statistical models using the flexible MLE framework within Stata.