Analysis Of Cross-Classified Data Research Articles

The Analysis of Contingency Tables: From Chi-Squared Tests and Log-Linear Models to Models of Mixed Membership

The roots of the modern log-linear model approach to the analysis of cross-classified data in the form of multi-dimensional contingency tables can found in the work of S. N. Roy and his students in the 1950s at the University of North Carolina. These papers set the stage for two major sets of developments in the analysis of categorical data in the 1960s and 1970s. I describe some of these contributions, where they intersected and where they diverged in focus, and some subsequent advances, including the role of latent variables alternatives, mixed membership models, and methods for very large sparse categorical data arrays.

A parameterized approach to modeling and forecasting mortality

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085–1111] or equivalently as a generalized Lee–Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751–2006) and Greece (1957–2006).

Statistical Models of Association for Comparing Cross-Classifications

In the analysis of cross-classified data, the quantities of interest are frequently odds ratios. Although odds ratios are functions of the interaction parameters in association models, the usual way of normalizing and identifying these parameters means that their relationship with the odds ratios of interest is indirect. This can lead to interpretative confusions. The author points to the benefits of defining the interaction parameters of a model to have a one-to-one relationship with the odds ratios of interest, thus overcoming problems of interpretation. Three examples are presented to illustrate the argument.

A Strategy for Designing Telescoping Models for Analyzing Multiway Contingency Tables Using Mixed Parameters

In the analysis of cross-classified data, sociologists often focus on building flexible models for the marginal distributions of a selected set of variables. One strategy for achieving flexible modeling is to design models for telescoping marginal distributions. As an illustration of telescoping distributions, consider a joint distribution of four crossclassifying variables: occupational attainment, education level, race, and gender. A set of telescoping distributions would be the univariate occupation distribution, the bivariate occupation by education, the trivariate occupation by education by race, and the entire joint distribution. A methodology that enables the telescoping modeling strategy is mixed parameterization, which has its roots in the statistics and sociology literatures. In this article, the authors develop a scheme of multilevel mixed parameterization that can be applied to a hierarchy of marginal distributions of reducing dimension. An example from the General Social Survey illustrates mixed parameters for telescoping models.

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Comment

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Rejoinder

Measures, Models, and Graphical Displays in the Analysis of Cross-Classified Data: Rejoinder

Discussion of the Papers by Edwards, and Wermuth and Lauritzen

Discussion of the Papers by Edwards, and Wermuth and Lauritzen

The Analysis of Cross-Classified Data Having Ordered Categories.

The Analysis of Cross-Classified Data Having Ordered Categories.

The Analysis of Cross-Classified Data Having Ordered Categories.

The Analysis of Cross-Classified Data Having Ordered Categories.

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered and/or Unordered Categories: Association Models, Correlation Models, and Asymmetry Models for Contingency Tables With or Without Missing Entries

The Analysis of Cross-Classified Data Having Ordered and/or Unordered Categories: Association Models, Correlation Models, and Asymmetry Models for Contingency Tables With or Without Missing Entries

The Analysis of Cross-Classified Data having Ordered Categories.

The Analysis of Cross-Classified Data having Ordered Categories.

Review of The Analysis of Cross-Classified Data Having Ordered Categories.

Review of The Analysis of Cross-Classified Data Having Ordered Categories.