Log-linear modelling for contingency tables by using marginal model structures
نویسنده
چکیده
An approach to log-linear modelling for a large contingency table is proposed in this paper. A main idea in this approach is that we group the random variables that are involved in the data into several subsets of variables with corresponding marginal contingency tables, build graphical log-linear models for the marginal tables, and then combine the marginal models using graphs of prime separators (section 2). When the true log-linear model for the whole table is decomposable, prime separators in a marginal model are also prime separators in a maximal combined model of the marginal models. This property plays a key role in model-combination. The result of the paper is applied to a simulated data set of 40 binary variables for illustration.
منابع مشابه
Conditional 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 کاملExploring dependence between categorical variables: Benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation...
متن کاملModeling conditional 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 demonstrates how marginal log-linear parameters can be used to measure this aspect of association. The paper gives a non-technical discussion of these two asp...
متن کاملBayesian Inference in Incomplete Multi-Way Tables
1 Summary We describe and illustrate approaches to Bayesian inference in multi-way contingency tables for which partial information, in the form of subsets of marginal totals, is available. In such problems, interest lies in questions of inference about the parameters of models underlying the table together with imputation for the individual cell entries. We discuss questions of structure relat...
متن کاملPlain Answers to Several Questions about Association/Independence Structure in Complete/Incomplete Contingency Tables
In this paper, we develop some results based on Relational model (Klimova, et al. 2012) which permits a decomposition of logarithm of expected cell frequencies under a log-linear type model. These results imply plain answers to several questions in the context of analyzing of contingency tables. Moreover, determination of design matrix and hypothesis-induced matrix of the model will be discusse...
متن کامل