Information and Complexity in Statistical Modeling
Information and Complexity in Statistical Modeling
复制标题
统计建模中的信息和复杂性
DOI：
10.1198/jasa.2008.s249
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发表时间：
2008
影响因子：
3.7
通讯作者：
Thomas C.M. Lee
中科院分区：
文献类型：
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作者：
Thomas C.M. Lee
作者显然对呈现材料的最佳方式进行了深入思考。所有概念都有明确的定义和很好的论证，并附有说明性示例。给出了所涵盖的所有主题的完整描述。大多数章节末尾都提供了练习，本书适合作为博士级实验设计课程的补充教材或主题阅读课程的正文。第一章解释了不同类型的陈述选择实验，插图很好地表明了该主题的重要性。进行此类实验的实际问题超出了本书的范围，但提供了参考资料。第 2 章对 2 阶和 3 阶析实验的构建进行了简短但完整的回顾。本章是本书中技术性最强的一章，读者可能会发现将其视为复习章节是有益的，因为他们已经在其他地方更悠闲地了解了详细信息。这一级别的设计背景材料可能只需要第 8 章，但自始至终都需要部分因子设计和因子效应对比的基本知识。第 3 章详细介绍了多项 Logit 模型，并探讨了选择实验设置的各种参数化。在此模型下，目标是选择最适合估计主效应以及两因素交互作用对比（如果需要）的实验设计。提到了几个最优准则，并选择了D-最优准则。 （D 最优设计最小化感兴趣对比的置信椭圆体的体积。）由于多项 Logit 模型是非线性模型，因此 D 最优设计取决于参数的真实值。作者没有考虑参数的合理范围以及最佳设计如何变化，而是在所有影响都可以忽略不计的零假设下获得了最佳设计。虽然有限制，但这是一个明智的选择，因为即使在这种情况下，理论上也不容易获得最佳设计。尽管如此，我希望在有先验信息的情况下看到对这些设计的稳健性进行彻底的调查。第 4 章给出了信息矩阵的非常仔细的推导，用于估计选择集的阶乘对比，其中所有属性都有两个级别（例如，高/低，或存在/不存在）。这些推导对组合要求很高，但结果很有趣且有用。例如，对于大小为 2 的选择集和主效应模型，由所有相互镜像的替代方案对组成的设计，例如（低、低、高）与（高、高、低）相比，是 D 最优的。竞争类设计仅由具有某些平衡属性的设计组成，而不是由所有可能的设计组成。所比较的设计具有不同数量的不同选择集，这与大多数设计情况不同。给出了获得高效小型设计的方法，以及避免主导替代方案的方法。第 3 章和第 4 章构成了本书的大部分基础知识。这两章的内容是独立的，但相当集中。如果我用这本书来教学，我会留出充足的时间来讨论这些材料。掌握了第 3 章中的多项 Logit 模型以及第 4 章中如何选择两水平 D 最优设计的知识后，读者可以更快地学习后续章节。第 5 章和第 6 章将第 4 章的结果扩展到大小为 m 的选择集（其中 m 是固定的且 >2），以及可能具有不同级别数的属性集。在每种情况下，都会获得 D 最优设计形式的具体要求，并给出有用的最优设计表。第 7 章和第 8 章通过讨论其他主题来完善本书。例如，考虑在每个选择集中包含“以上都不是”选项，并研究其对设计效率的影响。第 8 章探讨了为不同规模的实验构建最佳设计的方法；正是在这里，需要更详细的实验设计背景知识，例如第 2 章的背景知识。基本方法涉及选择起始设计 d ，并通过将生成器添加到 d 中的处理组合来创建选择集。对文献中发现的许多其他构建方法进行了比较，结果表明，在 D 最优性标准下，一般来说表现较差。然而，从 SAS 宏获得的设计在许多情况下似乎确实具有竞争力。本书对选择实验的 D 最优设计结构进行了出色的处理。我很喜欢阅读它，并希望包含有关第 7 章中简要介绍的主题的更多详细信息。我发现书中的印刷字体太小，不适合长期舒适地阅读，但这是一本优秀文本的唯一缺点。
The authors clearly have thought very deeply about the best way to present the material. All concepts are well defined and nicely argued and are followed by illustrative examples. Complete descriptions are given of all topics covered. Exercises are provided at the ends of most chapters, and the book is suitable as a supplemental text in a doctoral-level experimental design course or as the main text in a topics reading course. In Chapter 1 different types of stated choice experiments are explained, and the illustrations show the importance of the subject very well. Practical issues of running such experiments are beyond the scope of the book, but references are given. Chapter 2 gives a brief, but complete, review of the construction of fractional 2 and 3 factorial experiments. This chapter is the most technical one in the book, and readers may find it beneficial to consider it a review chapter, having learned the details at a more leisurely place elsewhere. Background material on design at this level likely is needed only for Chapter 8, but a basic knowledge of fractional factorial designs and factorial effects contrasts is needed throughout. Chapter 3 presents the multinomial logit model in detail, and various parameterizations for the choice experiment setting are explored. Under this model, the objective is to select a design for an experiment that is optimal for estimating the main effects and, if required, the two-factor interaction contrasts. Several optimality criteria are mentioned, and the D-optimality criterion is selected. (Doptimal designs minimize the volume of the confidence ellipsoid for the contrasts of interest.) Because the multinomial logit model is a nonlinear model, the D-optimal designs depend on the true values of the parameters. Rather than looking at plausible ranges of parameters and how the optimal designs vary, the authors obtain optimal designs under the null hypothesis that all effects are negligible. Although restrictive, this is a sensible choice because even in this situation, the optimal designs are not easy to obtain theoretically. Nonetheless, I would have liked to have seen a thorough investigation of robustness of these designs when prior information is available. Chapter 4 gives very careful derivations of the information matrices for estimating the factorial contrasts for choice sets in which all attributes have two levels (e.g., high/low, or present/absent). These derivations are combinatorially demanding, but the results are interesting and useful. For example, for choice sets of size 2 and main effects models, designs composed of all pairs of alternatives that are mirror images of each other, such as (low, low, high) compared with (high, high, low), are D-optimal. The competing class of designs is composed only of designs that have certain balance properties rather than all possible designs. The designs being compared have different numbers of distinct choice sets, which is different from most design situations. Methods of obtaining highly efficient smaller designs are given, together with ways of avoiding dominating alternatives. Chapters 3 and 4 form much of the groundwork of the book. The material in these two chapters is self-contained but fairly concentrated. If I were teaching from this book, I would allow ample time for covering this material. Having gained mastery of the multinomial logit model in Chapter 3 and knowledge of how to select a two-level D-optimal design in Chapter 4, the reader can then cover subsequent chapters more quickly. Chapters 5 and 6 extend the results of Chapter 4 to choice sets of size m, where m is fixed and >2, and to sets of attributes that may not have the same number of levels. In each case specific requirements for the form of the D-optimal designs are obtained and useful tables of optimal designs are presented. Chapters 7 and 8 round out the book by discussing additional topics. For example, the inclusion of a “none of the above” option in every choice set is considered, and its effect on the efficiency of the design is investigated. Methods of constructing optimal designs for different sized experiments are explored in Chapter 8; it is here that a more detailed background knowledge of experimental design, such as that of Chapter 2, is needed. The basic methodology involves selecting a starting design, d , and creating choice sets by adding generators to the treatment combinations in d . A number of other methods of construction found in the literature are compared and shown to perform less well in general under the D-optimality criterion. Designs obtained from the SAS macro do seem to be competitive in many settings, however. This book provides an excellent treatment of the structure of D-optimal designs for choice experiments. I enjoyed reading it and wished that more details on the topics covered briefly in Chapter 7 had been included. I found the print in the book too small for comfortable long-term reading, but this is the only drawback to an otherwise excellent text.