19,070 research outputs found
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
Implementing a Class of Permutation Tests: The coin Package
The R package coin implements a unified approach to permutation tests providing a huge class of independence tests for nominal, ordered, numeric, and censored data as well as multivariate data at mixed scales. Based on a rich and flexible conceptual framework that embeds different permutation test procedures into a common theory, a computational framework is established in coin that likewise embeds the corresponding R functionality in a common S4 class structure with associated generic functions. As a consequence, the computational tools in coin inherit the flexibility of the underlying theory and conditional inference functions for important special cases can be set up easily. Conditional versions of classical tests---such as tests for location and scale problems in two or more samples, independence in two- or three-way contingency tables, or association problems for censored, ordered categorical or multivariate data---can easily be implemented as special cases using this computational toolbox by choosing appropriate transformations of the observations. The paper gives a detailed exposition of both the internal structure of the package and the provided user interfaces along with examples on how to extend the implemented functionality.
Robust Principal Component Analysis for Compositional Tables
A data table which is arranged according to two factors can often be
considered as a compositional table. An example is the number of unemployed
people, split according to gender and age classes. Analyzed as compositions,
the relevant information would consist of ratios between different cells of
such a table. This is particularly useful when analyzing several compositional
tables jointly, where the absolute numbers are in very different ranges, e.g.
if unemployment data are considered from different countries. Within the
framework of the logratio methodology, compositional tables can be decomposed
into independent and interactive parts, and orthonormal coordinates can be
assigned to these parts. However, these coordinates usually require some prior
knowledge about the data, and they are not easy to handle for exploring the
relationships between the given factors.
Here we propose a special choice of coordinates with a direct relation to
centered logratio (clr) coefficients, which are particularly useful for an
interpretation in terms of the original cells of the tables. With these
coordinates, robust principal component analysis (PCA) is performed for
dimension reduction, allowing to investigate the relationships between the
factors. The link between orthonormal coordinates and clr coefficients enables
to apply robust PCA, which would otherwise suffer from the singularity of clr
coefficients.Comment: 20 pages, 2 figure
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