Factoring the likelihood function

Lindsey, J K

doi:10.1093/oso/9780198523598.003.0006

Chapter

6 Factoring the likelihood function

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https://doi.org/10.1093/oso/9780198523598.003.0006

Pages

233–275

Published:

May 1996

Abstract

The likelihood function provides an overall assessment of the relative merits of different members of a given family of statistical models, although this must be balanced against their relative complexity. However, as we saw in Section 3.6.3, we often require measures of precision of the estimates of individual parameters in the model. This is most often the case in a decision context (Part IV), where, for example, one might wish to decide which of two or more treatments provides the most positive effect, while controlling for various other influential factors. As in Section 3.6.3, the techniques to be discussed in this chapter should not be used for model selection, such as determining if a parameter could be set to zero. They are appropriate for interval estimation of individual parameters once an appropriate model has been selected. When the parameter vector is of low dimension, the precision of a parameter can be determined by inspecting a plot of the (profile) likelihood function. However, when many parameters are present in a statistical model, the profile likelihood will give a poor measure of the uncertainty in any one parameter component, unless it is orthogonal to the others, because it effectively assumes that the other parameter components are known to be equal to their maximum likelihood estimates (for fixed value of the parameter ofinterest). Thus, in Section 3.6.3, we introduced a modified profile likelihood to meet this problem, with a further application in Section 4.2.2. In this chapter, we shall explore in more detail the validity of such approximations.

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Contents

6 Factoring the likelihood function

Abstract

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6 Factoring the likelihood function

Abstract

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