Maura E. Stokes

Categorical Data Analysis: Some Reflections on the Log Linear Model and Logistic Regression. Part I: Historical and Methodological Overview*

Summary The literature of log linear models and logistic regression is surveyed from a contemporary point of view. A matrix formulation of the general log linear model for product-multinomial random counts is exploited to study the relationship between maximum likelihood and weighted least squares approaches to model fitting. Maximum likelihood fitted parameters and cell expectations are shown to be stationary solutions of a weighted least squares equation. Matrix expressions for asymptotic covariance matrices of efficient fitted parameters and cell counts are developed. Asymptotic covariance matrices of generalized raked contingency tables are obtained from the matrix formulation. Functional asymptotic regression methodology, an approach combining aspects of maximum likelihood and weighted least squares, is described and examined. In Part II, the several methods and relationships are illustrated by seven examples; extensions applicable to noncentrality problems and complex sample survey designs are also presented.

Some Views on Parametric and Non-Parametric Analysis for Repeated Measurements and Selected Bibliography

A common feature of many statistical investigations is the collection of data from groups of experimental units each of which is observed under two or more conditions. Such studies are generally called either split-plot experiments or repeated measurements experiments. This paper is concerned with reviewing general statistical strategies for the analysis of data from these types of research designs. For this purpose, primary attention is directed at two basic dimensions. One of these is the nature of the randomization processes for the data as obtained among and within the experimental units. The other is the level of the measurement scale as either nominal, ordinal, or interval. This framework is then used as the basis of discussion of alternative statistical methods such as repeated measurements analysis of variance, multivariate analysis of variance, and their non-parametric rank and categorical data counterparts in both a general sense and for some specific classes of examples. Finally, a selected bibliography of references for these and related methods is given.

A critical look at accumulation analysis and related methods

Industrial quality characteristics are often measured categorically rather than numerically, such as by recording a response as “slight,” “moderate,” or “extreme.” Accumulation analysis, a method proposed by Taguchi (1974) for analyzing ordered categorical data from industrial experiments, is used in Japanese industry and is becoming popular in the United States. Nair (1986) proposed using the first two components of the accumulation analysis statistic separately, as well as using simpler alternatives, to detect location and dispersion effects, respectively. We expose some problems with accumulation analysis in the multifactor setting, which is the usual industrial setting, since it is more efficient to investigate many factors simultaneously. Our results show that accumulation analysis detects spurious factor effects and reverses the order of factor importance. Furthermore, reanalysis of data from two real experiments reveals that these problems with accumulation analysis are realized in practice. We dem...