Cross-classified Data Research Articles

The Analysis of Cross-Classified Data Having Ordered Categories

The Analysis of Cross-Classified Data Having Ordered Categories

Bayesian Analysis of a 2 × 2 Contingency Table with Both Completely and Partially Cross-Classified Data

A frequently used experimental design is one in which the experimental units are measured twice (e.g., under different test conditions). When the response variable is dichotomous, the equality of the two proportions is usually assessed by a test due to McNemar (1947) . However, in addition to obtaining this complete data where two responses are available for each unit, incomplete data may be available also: In this case observations are available on the first response alone for some units and additional observations are available on the second response alone for other units. In this paper Bayesian methods are presented for estimating and testing hypotheses regarding the two success probabilities in light of both the complete and incomplete data. A method by which the prior distribution may be assessed is sketched and a numerical example to illustrate the method is presented.

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

Bayesian Analysis of a 2 × 2 Contingency Table with Both Completely and Partially Cross-Classified Data

Bayesian Analysis of a 2 × 2 Contingency Table with Both Completely and Partially Cross-Classified Data

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.

Estimating the Variance of Empirical Logits and Contrasts in Empirical Log Probabilities

The estimation of contrasts in logits of binomial variates or in log probabilities of multinomial variates is often an integral part of an analysis of cross-classified or assay data. Several estimators of the logit have been proposed. The biases of four such estimators were computed by Gart and Zweifel (1967) and Cook (1977). Their numerical work supports the use of the Haldane-Anscombe empirical logit estimator for smalland moderate-sized samples. We propose a new general class of estimators of the variance of the HaldaneAnscombe empirical logit estimator; this includes the estimator due to Gart (1966) as a special case. Numerical comparisons indicate that certain members of this class are typically less biased than Gart's estimator. The proposed estimators are generalized to allow estimation of the variance of contrasts of empirical log probabilities with constant coefficients.

Berkson's bias and simpson's paradox are the same fallacy in the analysis of cross-classified categorical data

Berkson's bias and simpson's paradox are the same fallacy in the analysis of cross-classified categorical data

A Mosaic of Television Ratings

Abstract A mosaic is a graphical display of cross-classified data in which each count is represented by a rectangle of area proportional to the count. The positions and sides of the rectangles are set to encourage comparisons between counts in the figures. Mosaics are useful for discovering unusually high or small counts and for discovering dependencies between variables. In principle, mosaics may be used for any number of cross-classifying variables, but six seems to be a practical maximum. A mosaic is given for a four-way classification of Nielsen ratings.

Age-period-cohort analysis: an illustration of the problems in assessing interaction in one observation per cell data

This paper discusses the specific problems of age-period-cohort (A-P-C) analysis within the general framework of interaction assessment for two-way cross-classified data with one observation per cell. The A-P-C multiple classification model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the two-way table) is characterized as one of a special class of models involving interaction terms assumed to have very specific forms. The so-called A-P-C identification problem, which results from the use of a particular interaction structure for detecting cohort effects, is shown to manifest itself in the form of an exact linear dependency among the columns of the design matrix. The precise relationship holding among these columns is derived, as is an explicit formula for the bias in the parameter estimates resulting from an incorrect specification of an assumed restriction on the parameters required to solve the normal equations. Current methods for model...

Log-linear models, screening and regional industrial surveys

Upton G. J. G. (1981) Log-linear models, screening and regional industrial surveys, Reg. Studies 15, 33–45. This paper uses hierarchical log-linear models to analyse a set of cross-classified categorical data obtained from a recent regional industrial survey of Northern Ireland. The data constitute a complete 27 table. Selection of an appropriate model is facilitated by use of the screening technique advocated by Brown (1976). In the analysis a clear distinction is drawn between factors and responses, and attention is concentrated on locating the factor-response interactions of likely significance. The paper is intended as a companion to that of Wrigley (1980) who performs a logit analysis of the same data.

A Computer Program for Multidimensional Contingency Table Construction 1

A computer program (ALT) is presented as an aid in the analysis of cross-classified categorical data. Program ALT can accept a maximum of 500 variables as data and construct a frequency table of from 1 to 8 dimensions. Each variable may have as many as 8 categories. In addition, ALT can combine, recode, and create formal variables at the user's discretion.

A Scaling Model for Survey Monitoring

Social indicators work has been dominated by "objective" measures expressed in various physical units (for example, crime rates). The present work is part of an attempt to correct this imbalance by providing a method for monitoring subjective indicators over different demographic segments and time points. The present monitoring model, which is based on psychometric scaling theory, is also similar to models in test theory and choice theory, and its parameters are estimated noniteratively. A principal advantage of this model, when applied to survey rating scales, stems from built-in parameters which provide for its evaluation. This evaluation reveals encouraging results in the present applications of the model to cross-classified survey data. Other potential applications, including quasi- experimental methods, are also discussed.

Some Exploratory Methods for Modeling Mobility Tables and Other Cross-Classified Data

This research was supported by grants from the National Science Foundation (GI-31604 and GI-44336), the National Institute of Mental Health (MH06275), and the Institute for Research on Poverty at the University of WisconsinMadison under funds granted by the Equal Opportunity Act of 1964 and administered by the Department of Health, Education, and Welfare. It was written in part while the author was a Fellow at the Center for Advanced Study in the Behavioral Sciences with support from the National Institute of Mental Health, the Spencer Foundation, and the Graduate School of the University of Wisconsin-Madison. Peter J. Dickinson, Randy D. Hodson, and James Baron assisted in computations, using facilities of the Center for Demography and Ecology that are supported by a grant from the National Institute for Child Health and Human Development (HD-5876). I thank Otis Dudley Duncan, Leo A. Goodman, William Mason, Halliman H. Winsborough, Burton Singer, Harry P. Travis, Taissa S. Hauser, Randy D. Hodson, and Yossi Shavit for advice and criticism. Any

Components of Student-Faculty Evaluation Data

The students' perception of overall teaching performance is very strongly aligned with his feeling about the course. Cross-classified data enable the separation of the effects of the teacher, the course, and the individual student groups. All three effects are highly significant and the effect of the course is by far the most prominent. Moreover, the effect of the student group is more important than the effect of the instructor.

Reviews: Oldham CDP; An Assessment of its Impact and Influence on the Local Authority, the Management of Deprivation: Final Report of the Southwark Community Development Project, Models of Cities and Regions: Theoretical and Empirical Developments, the Analysis of Cross-Classified Categorical Data, Planning for Internal Migration: A Review of Issues and Policies in Developing Countries, the Economics of Housing Policy, Rural

Reviews: Oldham CDP; An Assessment of its Impact and Influence on the Local Authority, the Management of Deprivation: Final Report of the Southwark Community Development Project, Models of Cities and Regions: Theoretical and Empirical Developments, the Analysis of Cross-Classified Categorical Data, Planning for Internal Migration: A Review of Issues and Policies in Developing Countries, the Economics of Housing Policy, Rural

Log-Linear Models in Geography

This paper uses three examples taken from the geographical literature to illustrate the success of the Goodman approach using log-linear models to interpret cross-classified data. The data sets studied contain a variety of combinations of factors and responses with varying numbers of categories. They relate to models of spatial behaviour and to the incidence of chronic bronchitis in Cardiff.

Adjustment of rates using multiplicative models

By the conception of an underlying multiplicative model for cross-classified data, a statistical method for the adjustment of rates is suggested. This method rests upon the multiplicative definition of interaction in cross-classifications and can lead to results different from those obtained from the more usual methods (e.g., Kitagawa, 1964). Comparisons with alternative approaches are made, and illustrative applications to data are provided.

The Analysis of Unbalanced Cross-Classifications

the President Dr H. P. WYNN in the Chair) SUMMARY The problem of choosing appropriate models for multiply cross-classified data is examined. It is shown that a standard method of analysis used in many ANOVA programs, equivalent to Yates's method of weighted squares of means, may lead to inappropriate models. A simultaneous test procedure equivalent to one proposed in regression analysis is used to derive a class of acceptable models. The procedure is applied to an example. THIS paper presents a simple procedure for the analysis of multiply cross-classified data, for both normal and non-normal responses. The procedure is based on the hierarchical partition- ing of the total sum of squares or maximized likelihood, with a simultaneous test procedure, proposed in regression analysis, applied to the hierarchical partition to determine appropriate models for the data. This leads to a class of minimal adequate models; there may be several models in this class. The procedure is illustrated by applying it to a set of normal response data. Before discussing the general cross-classification, we consider some difficulties that have arisen in the treatment of the unbalanced two-way classification. 2. TIk TWO-WAY CLASSICATION 2.1. The2x2 Case Consider a 2 x 2 cross-classification with disproportionate subclass frequencies. We will be concerned with the case in which the disproportionality is considerable, so that approximate methods based on replacing the observed frequencies by proportional expected frequencies are inappropriate. Let A1, A2 and B1, B2 denote the levels of the cross-classifying factors, and let nU, j and ,uH be the sample size, and sample and population means in the (i,j) cell of the classifica- tion, and let n. and n 1 be the row and column marginal totals: B1 B2 B1 B2 B1 B2

On the Use of Double Sampling Schemes in Analyzing Categorical Data with Misclassification Errors

Abstract In order to resolve the difficulties involved in inference from a sample of categorical data obtained by using a fallible classifying mechanism (usually inexpensive), we consider, as in Tenenbein (1970, 1971, 1972), the utilization of an additional sample. The second sample is subjected to a simultaneous cross-classification of its elements by the fallible mechanism and by some true (usually expensive) classifying mechanism. The setup is general; i.e., the discussion can be applied to any multidimensional cross-classified data obtained by unrestricted random sampling. Two methodologies are presented: (i) a combined maximum likelihood (ML) and least squares (LS) approach and (ii) a complete-LS approach. Both methodologies are illustrated using real data.