Tutorial on maximum likelihood estimation

In this paper, I provide a tutorial exposition on maximum likelihood estimation (MLE). The intended audience of this tutorial are researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method. Unlike least-squares estimation which is primarily a descriptive tool, MLE is a preferred method of parameter estimation in statistics and is an indispensable tool for many statistical modeling techniques, in particular in non-linear modeling with non-normal data. The purpose of this paper is to provide a good conceptual explanation of the method with illustrative examples so the reader can have a grasp of some of the basic principles.

[1]  J. Wixted,et al.  On the Form of Forgetting , 1991 .

[2]  D. Rubin,et al.  One Hundred Years of Forgetting : A Quantitative Description of Retention , 1996 .

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  I. J. Myung,et al.  The Importance of Complexity in Model Selection. , 2000, Journal of mathematical psychology.

[5]  T. Wickens On the form of the retention function : Comment on Rubin and Wenzel (1996) : A quantitative description of retention , 1998 .

[6]  Roger Ratcliff,et al.  A Theory of Memory Retrieval. , 1978 .

[7]  James L. McClelland,et al.  The time course of perceptual choice: the leaky, competing accumulator model. , 2001, Psychological review.

[8]  K. Lamberts Information-accumulation theory of speeded categorization. , 2000, Psychological review.

[9]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[10]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[11]  William H. Batchelder,et al.  Multinomial processing tree models of factorial categorization , 1997 .

[12]  B. Murdock,et al.  The retention of individual items. , 1961, Journal of experimental psychology.

[13]  T. Zandt,et al.  How to fit a response time distribution , 2000, Psychonomic bulletin & review.

[14]  Aris Spanos,et al.  Probability theory and statistical inference: econometric modelling with observational data , 1999 .

[15]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[16]  Walter L. Smith Probability and Statistics , 1959, Nature.

[17]  I. J. Myung,et al.  GUEST EDITORS' INTRODUCTION: Special Issue on Model Selection , 2000 .

[18]  I. J. Myung,et al.  Toward a method of selecting among computational models of cognition. , 2002, Psychological review.

[19]  D. Rubin,et al.  The Precise Time Course of Retention , 1999 .