Treatment of the Fourfold Table by Partial Association and Partial Correlation as it Relates to Public Health Problems

Lombard, Herbert L.; Doering, Carl R.

doi:10.2307/3001947

Cited by 14 publications

(15 citation statements)

References 2 publications

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“…In this study 1,729 people were cross-classified according to whether they had good or poor knowledge about cancer (the response variable), did "solid" reading, listened to the radio, attended lectures, and read the newspaper. This example was originally presented by Dyke and Patterson (1952) and is based on an observational study of Lombard and Doering (1947). The data were also analyzed by Fienberg (1980) and Goodman (1970), both of whom listed the 25 table.…”

Section: Examples and Summary Of Major Findingsmentioning

confidence: 99%

Evaluating Logistic Models for Large Contingency Tables

Fowlkes

Freeny

Landwehr

1988

Journal of the American Statistical Association

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This article discusses through three examples several new methods to aid in the analysis of large contingency tables. The general goal is to give better understanding of specific contingency tables, both by comparing how various log-linear/logistic models fit and through clearer interpretations of the resulting fits. For model selection, we show how to focus on a subset of simple, good-fitting models, beginning with a plot of a goodness-of-fit statistic versus residual degrees of freedom for all of the fitted models. To assess whether a particular model is adequate, we demonstrate that certain plots of residuals can reveal interesting effects that are often otherwise hidden. For model summarization and interpretation, we plot odds-ratio factors with confidence intervals to show the effects of explanatory variables in a concise and appealing way. The first example involves the relationship of job satisfaction to demographic variables for craft employees of a large corporation. The data presented consist of a fiveway contingency table with about 10,000 counts. Job satisfaction for such employees increased with age and was higher in the Southwest and West than in the Northeast. Of four race-by-sex groups, the most satisfied was nonwhite males; the least satisfied was nonwhite females. Another example gives a six-way table with about 1,200 counts concerning whether or not high-school students think they will need mathematics in their future work. Among other results, for students planning to take a job right after graduation, those from suburban schools had odds about 2.6 times those from urban schools of thinking that mathematics will be useful. Moreover, among urban students, males had odds of finding mathematics useful about 2.1 times those for females, but there was little difference between the odds for males and females among suburban students. The third example, drawn from the literature, relates knowledge about cancer to four dichotomous variables. We compare our analysis with earlier ones.

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Section: Examples and Summary Of Major Findingsmentioning

confidence: 99%

Evaluating Logistic Models for Large Contingency Tables

Fowlkes

Freeny

Landwehr

1988

Journal of the American Statistical Association

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“…The third set of data comes from a study on knowledge about cancer by Lombard & Doering (1947). A total of 1729 individuals were asked about whether or not they used the following sources of general information: radio, newspaper, solid reading and lectures.…”

Section: Cancer Knowledgementioning

confidence: 99%

Bootstrapping latent variable models for binary response

Albanese

Knott

1994

Brit J Math & Statis

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Estimated asymptotic variances for the estimates of the parameters in a logit-probit model for binary response data are unreliable for moderate sized samples. We show how bootstrapping gives a bctter idea of the sampling distribution of the estimators, and can also allow an assessment of the reliability of the scoring of individuals on the latent scale. lntroductionWhen a one-factor logit-probit model is fitted by maximum likelihood to binary (0, I ) response data, one very often wishes to score the observed response patterns on the scale of the latent variable. We prefer to score with the estimated conditional mean of the latent variable for the given response pattern, though Bartholomew (1984) has suggested scoring the response patterns by their component scores: thesc are defined as the sum of the estimated discrimination parameters for items responding 1. A difficulty with both methods of scoring is that little is known about the sampling properties of the estimators of the discrimination parameters. Usually one depends on the first-order asymptotic distribution theory for maximum likelihood estimators which suggests that the discrimination parameters have a sampling distribution which is asymptotically normal. The covariance matrix of the estimators is estimated from the observed information matrix. For logit-probit models for binary response with their usually large number of parameters it is not clear that sample sizes are great enough in practice to justify the use of this procedure. One would like to know whether the distributions of the estimators are approximately normal. One also needs a guide to the reliability of the scoring of the response patterns, and this is difficult to obtain from standard asymptotic theory.A common way to investigate questions of this type when exact mathematical results are not feasible is to generate bootstrap samples, and use these as a substitute for the t Requests for reprints

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“…Set I is taken from Lombard and Doering (1947)and it relates to knowledge about cancer. A sample of 1729 individuals were classified on four dimensions concerning sources of general knowledge each having two categories as follows: (1) Radio/no radio; (2) Newspapers/no newspapers; (3) Solid reading/no solid reading; (4) Lectures/no lectures.…”

Section: (25)mentioning

confidence: 99%

Factor Analysis for Categorical Data

Bartholomew

1980

Journal of the Royal Statistical Society Series B: Statistical Methodology

139

100

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Summary The method of factor analysis is widely used as an exploratory tool to reduce the dimensionality of multivariate data. The fact that the standard model is strictly applicable only when the manifest variables are scaled is a serious limitation in social science where the variables are often categorical. In this paper we aim to provide a theoretical framework within which methods for the factor analysis of categorical data can be devised and compared. Discussion is restricted to the case of ordered categories where the latent variables are continuous. It is argued that the choice of model should be made from a restricted set which includes two existing models as special cases. A new method is proposed together with a simple approximate technique of fitting for the one‐factor model. The paper concludes with an evaluation of existing methods and makes some suggestions about the direction which future research should take.

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Treatment of the Fourfold Table by Partial Association and Partial Correlation as it Relates to Public Health Problems

Cited by 14 publications

References 2 publications

Evaluating Logistic Models for Large Contingency Tables

Evaluating Logistic Models for Large Contingency Tables

Bootstrapping latent variable models for binary response

Factor Analysis for Categorical Data

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