Computing p-values in conditional independence models for a contingency table
نویسندگان
چکیده
We present a Markov chain Monte Carlo (MCMC) method for generating Markov chains using Markov bases for conditional independence models for a fourway contingency table. We then describe a Markov basis characterized by Markov properties associated with a given conditional independence model and show how to use the Markov basis to generate random tables of a Markov chain. The estimates of exact p-values can be obtained from random tables generated by the MCMC method. Numerical experiments examine the performance of the proposed MCMC method in comparison with the χ approximation using large sparse contingency tables.
منابع مشابه
AN OPTIMALITY THEORY FOR MID p–VALUES IN 2 × 2 CONTINGENCY TABLES
The contingency table arises in nearly every application of statistics. However, even the basic problem of testing independence is not totally resolved. More than thirty–five years ago, Lancaster (1961) proposed using the mid p–value for testing independence in a contingency table. The mid p–value is defined as half the conditional probability of the observed statistic plus the conditional prob...
متن کاملResidual-based Shadings for Visualizing (Conditional) Independence
Residual-based shadings for enhancing mosaic and association plots to visualize independence models for contingency tables are extended in two directions: (a) perceptually uniform Hue-Chroma-Luminance (HCL) colors are used and (b) the result of an associated significance test is coded by the appearance of color in the visualization. For obtaining (a), a general strategy for deriving diverging p...
متن کاملGraphical Log-Linear Models: Fundamental Concepts and Applications
We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of contingency tables involving several factors or categorical variables is very hard. To determine interactions among various factors, graphical and decomposable l...
متن کاملConditional and marginal association in contingency tables
Standard tools for the analysis of the (average) conditional association structure of the distribution on a multiway contingency table are log-linear models. A different association concept is that of marginal association and this paper describes how marginal log-linear parameters can be used to measure this aspect of association. The paper gives a non-technical discussion of these two aspects ...
متن کاملHierarchical subspace models for contingency tables
For statistical analysis of multiway contingency tables we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving conditional independence structures in the hierarchical model. We discuss estimation and exacts tests of ...
متن کامل