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By B. J. T. Morgan (auth.)

ISBN-10: 0412317508

ISBN-13: 9780412317507

ISBN-10: 1489945393

ISBN-13: 9781489945396

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Exercises marked with a * are generally more difficult or speculative. 1 Identify at least three examples of quantal response data which do not arise from toxicology or efficacy studies. 3t The following data sets were part of a collection put together by Copenhaver and Mielke (1977), and analysed also by Morgan (1985). Each set is given in the form: dose, dosage, concentration (or transformation of this), number responding, number in experiment. Details of dose transformations are given in Copenhaver and Mielke (1977, Table 1) and the raw data are given in Egger (1979), who excluded data set 14 on account of response being partly due to natural mortality.

19). 7 Discussion The material of this chapter provides an introduction to the work of later chapters. g. the probit transformation, with 1 F(z) = ~- -/be fz e- "'-x 2 2 dx -oo which has slightly lighter tails than the logistic form, the sine curve, with . n n F(z)={1+sm(z)} for --:(;z:(;- 2 2 and the Cauchy cumulative distribution function, 1 -1(z), 10r c F(z) = 21 +-tan - oo < z < oo n 28 DATA, PRELIMINARY ANALYSES AND MECHANISTIC MODELS sometimes called Urban's curve. Appropriate graphs are given in Ashton (1972, p.

In general terms we may describe models as mechanistic or descriptive (in the latter case, Ripley, 1987, prefers the term convenient). The latter type of model does not rely on a specification of a mechanism, and simply aims to summarize the data, and provide a framework for inference. Thus we may regard a simple linear regression model as descriptive. The end-product of a mechanistic modelling exercise may be a descriptive model, whose parameters play no role other than fitting the model to the data, and we shall encounter several examples of this.

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Analysis of Quantal Response Data by B. J. T. Morgan (auth.)

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