115 research outputs found
The Geometry of Statistical Models for Two-Way Contingency Tables with Fixed Odds Ratios
We study the geometric structure of the statistical models for two-by-two
contingency tables. One or two odds ratios are fixed and the corresponding
models are shown to be a portion of a ruled quadratic surface or a segment.
Some pointers to the general case of two-way contingency tables are also given
and an application to case-control studies is presented.Comment: References were not displaying properly in the previous versio
Markov bases and structural zeros
AbstractIn this paper we apply the elimination technique to the computation of Markov bases, paying special attention to contingency tables with structural zeros. An algebraic relationship between the Markov basis for a table with structural zeros and the corresponding complete table is proved. In order to find the relevant Markov basis, it is enough to eliminate the indeterminates associated with the structural zeros from the toric ideal for the complete table. Moreover, we use this result for the computation of Markov bases for some classical log-linear models, such as quasi-independence and quasi-symmetry, and computations in the multi-way setting are presented
Outliers and patterns of outliers in contingency tables with Algebraic Statistics
In this paper we provide a definition of pattern of outliers in contingency
tables within a model-based framework. In particular, we make use of log-linear
models and exact goodness-of-fit tests to specify the notions of outlier and
pattern of outliers. The language and some techniques from Algebraic Statistics
are essential tools to make the definition clear and easily applicable. Some
numerical examples show how to use our definitions.Comment: 24 pages, several examples and comments added in this versio
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