The Analysis of Binary Data
Plackett, R. L.
2018-12-05 00:00:00
1971] Reviews subject is welcome. As might have been expected from the authors, their approach is well presented, technically admirable and down to earth in the sense of being illustrated by practical examples. No practitioner in time-series analysis can afford to ignore it. The authors would, I think, be the first to admit that the question whether their methods represent an advance on more traditional approaches is one that we must each decide for ourselves in the light of experience of our own particular fields. M. G. KENDALL Scientific Control Systems Ltd 3. The Analysis of Binary Data. By D. R. Cox. London, Methuen, 1970. viii, 142 p. Sf'. £2. Binary or quantal data result when an experiment consists of individual trials, at each of which there are just two possible outcomes, known as success and failure. The probability of success usually depends on explanatory variables and treatment combinations. When measurements are made on a continuous scale, the use of normal-theory linear models is well established. This monograph presents a comparable unified approach to the analysis of binary data by the use of linear models for the logistic transform of the probability of success. An introductory chapter provides examples to motivate the methods. The question of an appropriate statistical model is next considered. After the rejection of a linear model for the probabilities, the linear logistic model is defined, and the forms appropriate in different experimental situations are given. Alternative scales are briefly examined. There follows an asymptotically efficient analysis by weighted least squares, using associated techniques such as half-normal plotting. The analysis is based on the empirical logistic transform, suitably modified. Two modifications are given: the first removes the singularities which arise when there are no successes or no failures; and the second provides unbiased estimating equations. Fully efficient methods for finite samples are now considered. They arise from the existence of sufficient statistics, and the optimum properties of inferences conditional on fixed values for all but one of these statistics. A general theory is developed and applied to a wide range of problems. Further procedures of an asymptotically efficient nature are next discussed. They fall into two groups: the first is based on the empirical logistic transform and unbiased estimating equations; and the second on maximum likelihood and a hierarchical system of models. Particular attention is given to the graphical analysis of residuals. The final chapter is a miscellany of topics, which are treated by summarizing the appropriate methods. A set of 50 exercises contains many further results. The book is completed with a classified bibliography and indexes by author and subject. Another book from Professor Cox is always welcome, and the many statisticians who have studied his papers in this field will appreciate the convenience of a systematic account. The approach that he has chosen is a blend of mathematical and applied statistics where just enough of the theory is given to support a complete analysis of the numerical examples. Thus the book has much to offer a wide variety of readers, and its style is clear and informative throughout. When the time comes for a second edition, the last chapter could perhaps be made more attractive by examples of the kind which make earlier chapters so lucid. R. L. PLACKETT University of Newcastle upon Tyne 4. Probability and Statistical Inference. By R. G. Krutchkoff. New York, Gordon & Breach, 1970. xiv, 291 p. Sr'. £5·25. This book follows a fairly well-worn path through the laws of probability, distributions, generating functions and other topics in probability theory, followed by estimation theory
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngJournal of the Royal Statistical Society Series A (Statistics in Society)Oxford University Presshttp://www.deepdyve.com/lp/oxford-university-press/the-analysis-of-binary-data-qaKkz0ngCD
1971] Reviews subject is welcome. As might have been expected from the authors, their approach is well presented, technically admirable and down to earth in the sense of being illustrated by practical examples. No practitioner in time-series analysis can afford to ignore it. The authors would, I think, be the first to admit that the question whether their methods represent an advance on more traditional approaches is one that we must each decide for ourselves in the light of experience of our own particular fields. M. G. KENDALL Scientific Control Systems Ltd 3. The Analysis of Binary Data. By D. R. Cox. London, Methuen, 1970. viii, 142 p. Sf'. £2. Binary or quantal data result when an experiment consists of individual trials, at each of which there are just two possible outcomes, known as success and failure. The probability of success usually depends on explanatory variables and treatment combinations. When measurements are made on a continuous scale, the use of normal-theory linear models is well established. This monograph presents a comparable unified approach to the analysis of binary data by the use of linear models for the logistic transform of the probability of success. An introductory chapter provides examples to motivate the methods. The question of an appropriate statistical model is next considered. After the rejection of a linear model for the probabilities, the linear logistic model is defined, and the forms appropriate in different experimental situations are given. Alternative scales are briefly examined. There follows an asymptotically efficient analysis by weighted least squares, using associated techniques such as half-normal plotting. The analysis is based on the empirical logistic transform, suitably modified. Two modifications are given: the first removes the singularities which arise when there are no successes or no failures; and the second provides unbiased estimating equations. Fully efficient methods for finite samples are now considered. They arise from the existence of sufficient statistics, and the optimum properties of inferences conditional on fixed values for all but one of these statistics. A general theory is developed and applied to a wide range of problems. Further procedures of an asymptotically efficient nature are next discussed. They fall into two groups: the first is based on the empirical logistic transform and unbiased estimating equations; and the second on maximum likelihood and a hierarchical system of models. Particular attention is given to the graphical analysis of residuals. The final chapter is a miscellany of topics, which are treated by summarizing the appropriate methods. A set of 50 exercises contains many further results. The book is completed with a classified bibliography and indexes by author and subject. Another book from Professor Cox is always welcome, and the many statisticians who have studied his papers in this field will appreciate the convenience of a systematic account. The approach that he has chosen is a blend of mathematical and applied statistics where just enough of the theory is given to support a complete analysis of the numerical examples. Thus the book has much to offer a wide variety of readers, and its style is clear and informative throughout. When the time comes for a second edition, the last chapter could perhaps be made more attractive by examples of the kind which make earlier chapters so lucid. R. L. PLACKETT University of Newcastle upon Tyne 4. Probability and Statistical Inference. By R. G. Krutchkoff. New York, Gordon & Breach, 1970. xiv, 291 p. Sr'. £5·25. This book follows a fairly well-worn path through the laws of probability, distributions, generating functions and other topics in probability theory, followed by estimation theory
Journal
Journal of the Royal Statistical Society Series A (Statistics in Society)
– Oxford University Press
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