THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

25. Multiple Imputation for Nonresponse in Surveys. By D. B. Rubin. ISBN 0 471 08705 X. Wiley, Chichester, 1987. 258 pp. £30.25.

Multiple Imputation for Nonresponse in Surveys

Generalized Linear Models (2nd ed.)

Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

Experimental design

Survey experiments are a core tool for causal inference. Yet, the design of classical survey experiments prevents them from identifying which components of a multidimensional treatment are influential. Here, we show how conjoint analysis, an experimental design yet to be widely applied in political science, enables researchers to estimate the causal effects of multiple treatment components and assess several causal hypotheses simultaneously. In conjoint analysis, respondents score a set of alternatives, where each has randomly varied attributes. Here, we undertake a formal identification analysis to integrate conjoint analysis with the potential outcomes framework for causal inference. We propose a new causal estimand and show that it can be nonparametrically identified and easily estimated from conjoint data using a fully randomized design. The analysis enables us to propose diagnostic checks for the identification assumptions. We then demonstrate the value of these techniques through empirical applications to voter decision making and attitudes toward immigrants.

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Causal Inference in Conjoint Analysis: Understanding Multidimensional Choices via Stated Preference Experiments

The study of good nonregular fractional factorial designs has received significant attention over the last two decades Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs Moreover, some of these designs are found to have maximum projectivity among all designs

A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions

Multiple outcomes are increasingly used to assess chronic disease progression. We discuss and show how desirability functions can be used to assess a patient overall response to a treatment using multiple outcome measures and each of them may contribute unequally to the final assessment. Because judgments on disease progression and the relative contribution of each outcome can be subjective, we propose a data-driven approach to minimize the biases by using desirability functions with estimated shapes and weights based on a given gold standard. Our method provides each patient with a meaningful overall progression score that facilitates comparison and clinical interpretation. We also extend the methodology in a novel way to monitor patients’ disease progression when there are multiple time points and illustrate our method using a longitudinal data set from a randomized two-arm clinical trial for scleroderma patients.

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Data-driven desirability function to measure patients’ disease progression in a longitudinal study

A smooth response surface algorithm is developed as an elaborate data mining technique for analyzing gene expression data and constructing gene regulatory network. A three-dimensional smooth response surface is generated to capture the biological relationship between the target and activator-repressor. This new technique is applied to functionally describe triplets of activators, repressors and targets, and their regulations in gene expression data. A diagnostic strategy is built into the algorithm to evaluate the scores of the triplets so that those with low scores are kept and a regulatory network is constructed based on this information and existing biological knowledge. The predictions based on the identified triplets in two yeast gene expression data sets agree with some experimental data in the literature. It provides a novel model with attractive mathematical and statistical features that make the algorithm valuable for mining expression or concentration information, assist in determining the function of uncharacterized proteins, and can lead to a better understanding of coherent pathways.

A smooth response surface algorithm for constructing gene regulatory network

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066--1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman--Kempthorne construction of orthogonal arrays, several classes of optimal multi-level supersaturated designs are given in explicit form: Columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties.

Construction of optimal multi-level supersaturated designs

This paper considers the construction of minimum aberra- tion (MA) blocked factorial designs. Based on coding theory, the con- cept of minimum moment aberration due to Xu (2003) for unblocked designs is extended to blocked designs. The coding theory approach studies designs in a row-wise fashion and therefore links blocked designs with nonregular and supersaturated designs. A lower bound on blocked wordlength pattern is established. It is shown that a blocked design has MA if it originates from an unblocked MA design and achieves the lower bound. It is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros. Sufficient conditions are given for constructing MA blocked designs from unblocked MA designs. The theory is then applied to construct MA blocked designs for all 32 runs, 64 runs up to 32 factors, and all 81 runs with respect to four combined wordlength patterns.

Hongquan Xu

Papers

A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions

Data-driven desirability function to measure patients’ disease progression in a longitudinal study

A smooth response surface algorithm for constructing gene regulatory network

Construction of optimal multi-level supersaturated designs

Blocked Regular Fractional Factorial Designs With Minimum Aberration