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Practical Maximum Likelihood Altman, Micah McDonald, Michael P. Uploaded 07-22-2001 Keywords maximum likelihood optimization statistical computation numerical stability accuracy Abstract Maximum likelihood estimation is now widely used in political science, providing a general statistical framework in which we build and test increasingly complex models of politics. The modern development of maximum likelihood is attributable to Fisher, and the approach dominated mathematical statistics during the twentieth century. More attention has been paid to the development of complex statistical models than to the necessary details of their estimation. In this article we discuss some of the art and practice of MLE: -Estimation: We discuss how to choose algorithms for MLE estimations, methods for setting algorithm parameters appropriately, and how to formulate likelihood functions for efficient and accurate estimation. -Tests of Estimation: Methods of statistical inference assume that a global maximum of the likelihood function has been found. There are however, few general guarantees that likelihood functions are single-peaked. Furthermore, no MLE software currently in use by political scientists verifies that global maximum of the likelihood function has been reached. We provide tests of global optimality, drawing from current research in statistics, econometrics, and computer science. -MLE Based Inference: Standard errors produced by MLE's can be misleading, and lead to unreliable inferences, when the likelihood function is not well behaved around its maximum. We illustrate the consequences of unreliable methods, and discuss more robust methods of calculating