Graphical 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 log-linear models are preferred. First, we explore connections between the conditional independence in probability and graphs; thereafter we provide a few illustrations to describe how graphical log-linear model are useful to interpret the conditional independences between factors. We also discuss the problem of estimation and model selection in decomposable models

Markov chain Monte Carlo tests for designed experiments

We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, a Markov chain Monte Carlo method can be used for performing exact tests, when large-sample approximations are poor and the enumeration of the conditional sample space is infeasible. For designed experiments with a single observation for each run, we formulate log-linear or logistic models and consider a connected Markov chain over an appropriate sample space. In particular, we investigate fractional factorial designs with $2^{p-q}$ runs, noting correspondences to the models for $2^{p-q}$ contingency tables

Binary Models for Marginal Independence

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions

Conditional symmetry model as a better alternative to Symmetry Model for rater agreement measure

In almost all life or social science researches, subjects are classified into categories by raters, interviewers or observers. Many approaches have been proposed by various authors for analyzing the data or the results obtained from these raters. Symmetry and conditional symmetry models are models designed for square tables like the one arising from the raters results. Conditional symmetry model which possessed an extra parameter for the off-diagonal cells is a special case to symmetry. In this research work, we examined the effect of the extra parameter introduced by conditional symmetry model over that of symmetry on structure of agreement as well as their fittings. Generalized linear model (GLM) approach was used to model the loglinear model forms of these models with empirical examples. We observed that conditional symmetry based on it extra parameter gave a tremendous improvement to the significant level of the test statistics over that of its symmetry model counterpart, hence conditional symmetry model is better for raters agreement modelling which require symmetric table

The statistical relationship between product life cycle and repeat purchase behavior in convenience stores

The density function of product life cycles in convenience stores is found to follow the Weibull distribution. To clarify the parameters that determine these life cycles, we introduce the conditional market share-defined as the probability that a product is selected by customers only if it had been previously purchased-and the market share without any conditions. The product life cycle is more strongly correlated with the conditional market share of the product than with the latter type of market share.Comment: 9 pages, 5 figures, 3 tables. Progress of Theoretical Physics, in pres