2003 ModellingBinaryData

(Collett, 2003) ⇒ David Collett. (2003). “Modelling Binary Data, 2nd edition." CRC Press. ISBN:1584883243

Subject Headings: Binomial Distribution, Linear Logistic Model, Model Checking, Overdispersion, Exact Method.

Notes

Earlier edition in (1991) ISBN:0412387905

Cited By

Quotes

Publisher's Abstract

Since the original publication of the bestselling Modelling Binary Data, a number of important methodological and computational developments have emerged, accompanied by the steady growth of statistical computing. Mixed models for binary data analysis and procedures that lead to an exact version of logistic regression form valuable additions to the statistician's toolbox, and author Dave Collett has fully updated his popular treatise to incorporate these important advances. Modelling Binary Data, Second Edition now provides an even more comprehensive and practical guide to statistical methods for analyzing binary data. Along with thorough revisions to the original material-now independent of any particular software package- it includes a new chapter introducing mixed models for binary data analysis and another on exact methods for modelling binary data. The author has also added material on modelling ordered categorical data and provides a summary of the leading software packages. All of the data sets used in the book are available for download from the Internet, and the appendices include additional data sets useful as exercises.

1. Introduction p.1

Data in the form of proportions are often, but not exclusively, modelled using the binomial distribution, while binary data may be assumed to have the Bernoulli distribution, a special case of the binomial distribution. Methods for analysing what are often referred to as binary or binomial data are the subject of this book.

2. Statistical inference for binary data p.19

2.1 The binomial distribution

Consider a particular binary response that is either a success or a failure. … supposing that there is a probability, [math]\displaystyle{ p }[/math], that the seed will germinate. This probability is termed the success probability or response probability, but it will of be unknown. … Whether or not the seed germinates can be described in terms of a quantity known as a random variable, which will be denoted by R.

3. Models for binary and binomial data p.45

4. Bioassay and some other applications p.103

5. Model checking p.129

6. Overdispersion p.195

7. Modelling data from epidemiological studies p.215

8. Mixed models for binary data p.269

9. Exact Methods p.303

The general approach to modelling binary data that has been described in Chapter 3 is based on the method of maximum likelihood. Parameters in a model of interest are estimated by maximizing the likelihood function (Section 3.7), and alternative models are compared using the deviance (Section 3.9). In particular, the significance of adding an explanatory variable to a model ca be assessed by comparing the change in deviance due to the addition of that variable with percentage points in the Chi-squared distribution. This result for the distribution of the deviance is an asymptotic property, the validity of which depends on the number of binary observations in the data base. If this is so small that there are some observed proportions with very small denominators, or proportions close to zero or unity, inferences based on the asymptotic distribution of the change in deviance may be unreliable. Corresponding inferences about the effect that explanatory variables have on the response probability will then be invalid.
Dramatic increases in computing power, coupled with efficient numerical methods, now allow exact estimates of parameters in a logistic regression model to be obtained, and exact test procedures can be used in the comparison of alternative models. This means that we no longer need to rely on the applicability of large sample results when analysing small data sets. These exact methods are the subject of this chapter, which begins by looking at the simplest of situations, the comparison of two proportions, using Fisher's exact test. Methods that generalize this result leading to exact logistic regression are then described and illustrated.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2003 ModellingBinaryData	David Collett			Modelling Binary Data, 2nd edition			http://books.google.com/books?id=LMRAIBEbdqsC			2003