12,171 research outputs found

    Minimal and minimal invariant Markov bases of decomposable models for contingency tables

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    We study Markov bases of decomposable graphical models consisting of primitive moves (i.e., square-free moves of degree two) by determining the structure of fibers of sample size two. We show that the number of elements of fibers of sample size two are powers of two and we characterize primitive moves in Markov bases in terms of connected components of induced subgraphs of the independence graph of a hierarchical model. This allows us to derive a complete description of minimal Markov bases and minimal invariant Markov bases for decomposable models.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ207 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    A Markov Basis for Conditional Test of Common Diagonal Effect in Quasi-Independence Model for Square Contingency Tables

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    In two-way contingency tables we sometimes find that frequencies along the diagonal cells are relatively larger(or smaller) compared to off-diagonal cells, particularly in square tables with the common categories for the rows and the columns. In this case the quasi-independence model with an additional parameter for each of the diagonal cells is usually fitted to the data. A simpler model than the quasi-independence model is to assume a common additional parameter for all the diagonal cells. We consider testing the goodness of fit of the common diagonal effect by Markov chain Monte Carlo (MCMC) method. We derive an explicit form of a Markov basis for performing the conditional test of the common diagonal effect. Once a Markov basis is given, MCMC procedure can be easily implemented by techniques of algebraic statistics. We illustrate the procedure with some real data sets.Comment: 15 page

    A review of some models for the analysis of contingency tables : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Statistics at Massey University

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    Some models proposed for the analysis of contingency tables are reviewed and illustrated with examples. These include standard loglinear models; models which are suitable for ordinal categorical variables such as ordinal loglinear, log­ multiplicative and logit models, and models based on an underlying distribution for the response; and models for incomplete and square tables. Estimation methods and inference are also discussed
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