Three centuries of categorical data analysis: Log-linear models and maximum likelihood estimation
By Stephen E. Fienberg, Alessandro Rinaldo. 2007
101 citations recorded by the source corpus.
The common view of the history of contingency tables is that it begins in 1900 with the work of Pearson and Yule, but in fact it extends back at least into the 19th century. Moreover, it remains an active area of research today. In this paper we give an overview of this history focussing on the development of log-linear models and their estimation via the method of maximum likelihood. Roy played a crucial role in this development with two papers co-authored with his students, Mitra and Marvin Kastenbaum, at roughly the mid-point temporally in this development. Then we describe a problem that eluded Roy and his students, that of the implications of sampling zeros for the existence of maximum likelihood estimates for log-linear models. Understanding the problem of non-existence is crucial to the analysis of large sparse contingency tables. We introduce some relevant results from the application of algebraic geometry to the study of this statistical problem.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/55f915a19e7a6b867281b064f83a0d436db4bf8c
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In Algebra and Number Theory
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Citations in the corpus
- Multivariate binomial/multinomial control chart (2014, background): “This is the sparsity phenomenon, which may lead to the nonexistence of MLEs (Fienberg and Rinaldo, 2007).”
- Nonlinear Discrete Optimization (2010, background): “Let us mention the papers [8], [22], and [36], and the references therein, as informative sources corresponding to these three lines of investigation.”