Contingency Table Data Research Articles

The Asymptotic Efficiency of Tests Using Misclassified Data in Contingency Tables

A simple expression is given for the approximate upper bound of the asymptotic relative efficiency of tests between nested loglinear models using misclassified data versus those using data with no classification errors. This efficiency depends on the probabilities of data being misclassified into the wrong cells of the contingency table. An example demonstrates that the loss of efficiency due to misclassification can be substantial.

Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques

Abstract This paper unites two different fields, survival and contingency table analysis, in a single analytical framework based on the log-linear model. We demonstrate that many currently popular approaches to modeling survival data, including the approaches of Glasser (1967), Cox (1972), Breslow (1972, 1974), and Holford (1976), can be handled by using existing computer packages developed for the log-linear analysis of contingency table data. More important, we demonstrate that the log-linear modeling system used to characterize counted data structures directly characterizes survival data as well. Counted data methodologies for testing and estimation are also applicable here. Much of the theoretical basis for this work has been independently derived by Holford (1980) and Aitkin and Clayton (1980). The emphasis in this paper is not to develop new methodologies, but rather to present new uses and interpretations for already familiar methodologies.

Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques

Abstract This paper unites two different fields, survival and contingency table analysis, in a single analytical framework based on the log-linear model. We demonstrate that many currently popular approaches to modeling survival data, including the approaches of Glasser (1967), Cox (1972), Breslow (1972, 1974), and Holford (1976), can be handled by using existing computer packages developed for the log-linear analysis of contingency table data. More important, we demonstrate that the log-linear modeling system used to characterize counted data structures directly characterizes survival data as well. Counted data methodologies for testing and estimation are also applicable here. Much of the theoretical basis for this work has been independently derived by Holford (1980) and Aitkin and Clayton (1980). The emphasis in this paper is not to develop new methodologies, but rather to present new uses and interpretations for already familiar methodologies.

The Fisher information matrix for log linear models arguing conditionally on observed explanatory variable

SUMMARY For Poisson or multinomial contingency table data the conditional distribution is product multinomial when conditioning on observed values of explanatory variables. Birch (1963) showed that under the restriction formed by keeping the marginal totals of one margin fixed at their observed values the Poisson, multinomial and product multinomial likelihoods are proportional and give the same estimates for common parameters in the log linear model. Here the inverses of the Fisher information matrices are shown to be identical over common parameters so that the asymptotic covariance matrices of the estimates correspond.

Comparing Partial Rank Order Correlations From Contingency Table Data

This article describes an asymptotic method for obtaining estimates of variance and covariance for partial rank order correlation coefficients based on contingency table data The approach used is an extension of the Grizzle, Starmer, and Koch technique for the analy sis of complex contingency tables The variance and co variance estimates may be used to test hypotheses concerning the partial correla tions

Logistic-normal distributions:Some properties and uses

The logistic transformation applied to a d -dimensional normal distribution produces a distribution over the d -dimensional simplex which can sensibly be termed a logistic-normal distribution. Such distributions, implicitly used in a number of recent applications, are here given a formal identity and some useful properties are recorded. A main aim is to extend the area of application from the restricted role as a substitute for the Dirichlet conjugate prior class in the analysis of multinomial and contingency table data to the direct statistical description and analysis of compositional and probabilistic data.

DSYSTM: A Basic Computer Program for the Causal Analysis of Contingency Data

DSYSTM is an interactive BASIC program designed to perform a linear-graph analysis of contingency table data. The method, which follows that described by Davis (1976), is termed " d-systems analysis." The program handles polytomous variables, both prior and dependent. Data may be submitted interactively or stored and appended as data-sets. The input consists of tables of frequencies or proportions and the output includes parameter estimates and test statistics. The program is especially suitable for the analysis of change models.

Modelling Conditional Probability

Many studies of the joint frequency of the initial and final conditions of weather elements such as cloud cover, visibility, rainfall or temperature attest to the importance of the initial event as a predictor of the later event. Most efforts have involved the actual collection of the data in contingency tables but there is a strong need for an analytical tool to estimate the conditional probabilities from more readily available climatic frequencies. By assuming the Markov process, and with the help of published tables detailing the bivariate normal distribution, a succinct two-parameter model, using the climatic frequencies in a single equation, has been developed to estimate conditional probabilities, of both frequent and rare events, within a few percentage points. The two parameters have been charted as direct functions of the probability of the initial event and the temporal persistence of the element.

A Note on the Weighted Least Squares Analysis of the Ries-Smith Contingency Table Data

The technique of general weighted least squares is shown to be a useful tool in the formulation and evaluation of certain models appropriate to data in the form of multidimensional contingency tables. This is demonstrated for the Ries-Smith [1963] data by fitting a series of linear regression models which are directed at determining that model which explains almost all of the statistically significant variation among the cell frequencies in terms of a minimum number of parameters. The spirit of this approach is analogous to that used in stepwise regression for continuous data. The test criteria are Wald statistics or minimum-Neyman-chi-square as described by Bhapkar and Koch [1968].

A Note on the Weighted Least Squares Analysis of the Ries-Smith Contingency Table Data

The technique of general weighted least squares is shown to be a useful tool in the formulation and evaluation of certain models appropriate to data in the form of multidimensional contingency tables. This is demonstrated for the Ries-Smith [1963] data by fitting a series of linear regression models which are directed at determining that model which explains almost all of the statistically significant variation among the cell frequencies in terms of a minimum number of parameters. The spirit of this approach is analogous to that used in stepwise regression for continuous data. The test criteria are Wald statistics or minimum-Neyman-chi-square as described by Bhapkar and Koch [1968].

The Comparison of Proportions: A Review of Significance Tests, Confidence Intervals and Adjustments for Stratification

Probably the most common quantitative problem in biological research involves the question of the presence or absence of a particular attribute. In its simplest form it reduces to a 2 x 2 table analysis or a test for the difference between two proportions; in a more complex form it may involve comparison of several proportions adjusted for an auxiliary variable. This paper reviews the theory and application of statistical analyses appropriate for such data. The theory is set forth in the general framework of logistic models as formulated by Cox [16, 21] (see also Rasch [60]). This analysis uses the notion of conditioning the distribution of the test statistic on the ancillary statistics, which implies, in most cases, the so-called fixed marginals analysis of contingency tables. Other theoretical formulations are also considered briefly. The paper is divided into three parts: the first deals with 2 x 2 tables, the second with the combination of 2 x 2 tables, and the last with the combination of 2 x t tables. The latter two subjects are closely related to the analyses of higher order interaction in contingency tables and the fitting of multivariate contingency table data. These subjects are treated only peripherally here: the former subject has been thoroughly reviewed recently by Plackett [58] and the latter subject has been treated by Bishop [7] whose paper contains an extensive bibliography. The excellent papers by Birch [5, 6] deal with many of the questions we discuss here. For additional references, see Cox [21].

On the Hypotheses of 'No Interaction' in Contingency Tables

The statistical analysis of data in multi-dimensional contingency tables is discussed in terms of appropriate underlying probability models. Emphasis is placed on the distinction between 'factors' (such as treatments or blocks) which have fixed marginal totals and 'responses' (such as category of performance) which have random marginal totals. Hence, four principal cases arise: (i) the 'multi-response, no factor' tables, (ii) the 'multi-response, uni-factor' tables, (iii) the 'multi-response, multifactor' tables, (iv) the 'uni-response, multi-factor' tables. For situations (i) and (ii), the concept of 'no interaction' is related to questions regarding the pattern of association among responses. However, for situation (iv), it is related to how factors combine (e.g., additively) to determine the response distribution. Finally, for situation (iii), both types of questions arise. For each of the different types of tables, the problem of formulating appropriate hypotheses of 'no interaction' is considered. The corresponding test statistics are based upon a general and computationally simple criterion of Wald [1943]. The suggested methods are illustrated with several numerical examples.

Selected Contributions to Parametric and Nonparametric Statistics

ALTHOUGH THERE is a slight duplication of the research reviewed in this chapter with that to be found in Chapters I and III, an effort has been made to include those contributions to statistical methodology that were thought to be of at least some interest and of some potential help to research workers in the behavioral sciences. The scope of this particular chapter is probably broader and perhaps less unified than that of any other in this issue of the REVIEW. In this chapter, the major objective is to furnish for the period from July 1, 1960, to July 1, 1963, a brief description both of the general developments in statistical inference and of the somewhat specific contributions that have been made to the theory and application of parametric and nonparametric tests of significanceespecially those tests involving only two samples. Consideration has also been given to citing important books, to describing advances realized in the treatment of data in contingency tables, and to mentioning certain developments in the methodology of multiple comparisons that have not been noted by Norton in Chapter III.