OPTIMAL DESIGNS FOR 2 k PAIRED COMPARISON EXPERIMENTS

In this paper we establish the form of the optimal paired comparison design when there are k attributes, each with two levels, for testing for main effects, for main effects and two factor interactions and for main effects and two and three factor interactions. In all cases we assume that all pairs with the same number of attributes different appear equally often. In this setting the D and A optimal designs for main effects are the foldover pairs and those for main effects and two factor interactions have pairs in which about half the attributes are different.     

Optimal design for discrete choice experiments

In this paper we derive locally optimal designs for discrete choice experiments. As in Kanninen (2002) we consider a multinomial logistic model, which contains various qualitative attributes as well as a quantitative one, which may range over a sufficiently large interval. The derived optimal designs improve upon those given in the literature, but have the feature that every choice set contains alternatives, which coincide in all but the quantitative attributes. The multinomial logistic model will then lead to a response behavior, which is apparently unrealistic.     

Rank-order choice-based conjoint experiments: Efficiency and design

In a rank-order choice-based conjoint experiment, the respondent is asked to rank a number of alternatives of a number of choice sets. In this paper, we study the efficiency of those experiments and propose a D-optimality criterion for rank-order experiments to find designs yielding the most precise parameter estimators. For that purpose, an expression of the Fisher information matrix for the rank-ordered conditional logit model is derived which clearly shows how much additional information is provided by each extra ranking step. A simulation study shows that, besides the Bayesian D-optimal ranking design, the Bayesian D-optimal choice design is also an appropriate design for this type of experiments. Finally, it is shown that considerable improvements in estimation and prediction accuracy are obtained by including extra ranking steps in an experiment.     

Construction on non-adaptive hypergeometric group testing desings for identifying at most two defectives

In the literature a systematic method of obtaining a group testing design is not available at present. Weideman and Raghavarao (1987a, b) gave methods for the construction of non - adaptive hypergeometric group testing designs for identifying at most two defectives by using a dual method. In the present investigation we have developed a method of construction of group testing designs from (i) Hypercubic Designs for t ≡ 3 (mod 6) and (ii) Balanced Incomplete Block Designs for t ≡ 1 (mod 6) and t ≡ 3 (mod 6). These constructions are accomplished by the use of dual designs. The designs so constructed satisfy specified properties and attained an optimal bound as discussed by Weidman and Raghavarao (1987a,b). Here it is also shown that the condition for pairwise disjoint sets of BIBD for t ≡ 1 (mod 6) given by Weideman and Raghavarao (1987b) is not true for all such designs.     

Nonparametric model checking for k-out-of-n systems

It is an important problem in reliability analysis to decide whether for a given k-out-of-n system the static or the sequential k-out-of-n model is appropriate. Often components are redundantly added to a system to protect against failure of the system. If the failure of any component of the system induces a higher rate of failure of the remaining components due to increased load, the sequential k-out-of-n model is appropriate. The increase of the failure rate of the remaining components after a failure of some component implies that the effects of the component redundancy are diminished. On the other hand, if all the components have the same failure distribution and whenever a failure occurs, the remaining components are not affected, the static k-out-of-n model is adequate. In this paper, we consider nonparametric hypothesis tests to make a decision between these two models. We analyze test statistics based on the profile score process as well as test statistics based on a multivariate intensity ratio and derive their asymptotic distribution. Finally, we compare the different test statistics.     

Partitioned difference families and almost difference sets

Partitioned difference families (PDFs) were first studied by Ding and Yin in conjunction with the construction of constant composition codes (CCCs). In 2008, Yin et al. presented the constructions of a number of infinite classes of PDFs based on known difference sets in GF(q). In this paper, we further investigate the constructions of PDFs by using known almost difference sets in GF(q), and establish some recursive constructions of PDFs. As their applications, we also get a number of perfect difference systems of sets (DSSs) over Z_q² with q odd prime.     

An optimal response adaptive biased coin design with k heteroscedastic treatments

For comparing treatments in clinical trials, Atkinson (1982) introduced optimal biased coins for balancing patients across treatment assignments by using D-optimality under the assumption of homoscedastic responses of different treatments. However, this assumption can be violated in many real applications. In this paper, we relax the homoscedasticity assumption in the k treatments setting with k>2. A general family of optimal response adaptive biased coin designs are proposed following Atkinson's procedure. Asymptotic properties of the proposed designs are obtained. Some advantages of the proposed design are discussed.     

Bounding the resampling risk for sequential Monte Carlo implementation of hypothesis tests

Sequential designs can be used to save computation time in implementing Monte Carlo hypothesis tests. The motivation is to stop resampling if the early resamples provide enough information on the significance of the p-value of the original Monte Carlo test. In this paper, we consider a sequential design called the B-value design proposed by Lan and Wittes and construct the sequential design bounding the resampling risk, the probability that the accept/reject decision is different from the decision from complete enumeration. For the B-value design whose exact implementation can be done by using the algorithm proposed in Fay, Kim and Hachey, we first compare the expected resample size for different designs with comparable resampling risk. We show that the B-value design has considerable savings in expected resample size compared to a fixed resample or simple curtailed design, and comparable expected resample size to the iterative push out design of Fay and Follmann. The B-value design is more practical than the iterative push out design in that it is tractable even for small values of resampling risk, which was a challenge with the iterative push out design. We also propose an approximate B-value design that can be constructed without using a specially developed software and provides analytic insights on the choice of parameter values in constructing the exact B-value design.     

The optimal size of choice sets in choice experiments

In this paper, we establish the optimal size of the choice sets in generic choice experiments for asymmetric attributes when estimating main effects only. We give an upper bound for the determinant of the information matrix when estimating main effects and all two-factor interactions for binary attributes. We also derive the information matrix for a choice experiment in which the choice sets are of different sizes and use this to determine the optimal sizes for the choice sets.     

Optimal partially replicated parallel-flats designs for 2×3 mixed factorial experiments

Augmenting additional repeated runs to an unreplicated factorial design provides an economical scheme of obtaining an unbiased estimate for the error variance based on pure replicates. The augmented partially replicated design usually performs satisfactorily in identifying truly active effects regardless of whether the effect sparsity principle holds. Liao and Chai (2009) proposed a set of sufficient conditions for a partially replicated two-level design to be D-optimal over the class of parallel-flats designs. In this article, we generalize their result to the 2^n₁×3^n₂ mixed factorial under D-, A- and E-optimality, and include the 2ⁿ and 3ⁿ symmetric factorials as special cases. In addition, some examples are given to illustrate the main results.     

Bias-reduced estimates for skewness, kurtosis, L-skewness and L-kurtosis

Estimates based on L-moments are less non-robust than estimates based on ordinary moments because the former are linear combinations of order statistics for all orders, whereas the later take increasing powers of deviations from the mean as the order increases. Estimates based on L-moments can also be more efficient than maximum likelihood estimates. Similarly, L-skewness and L-kurtosis are less non-robust and more informative than the traditional measures of skewness and kurtosis. Here, we give nonparametric bias-reduced estimates of both types of skewness and kurtosis. Their asymptotic computational efficiency is infinitely better than that of corresponding bootstrapped estimates.     

Choice experiments for estimating main effects and interactions

Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles and asked to select the one they consider best. However if choice sets have too many profiles, they may be difficult to implement. In this paper we provide strategies for reducing the number of profiles in choice sets. We consider situations where only a subset of interactions is of interest, and we obtain connected main effect plans with smaller choice sets that are capable of estimating subsets of two-factor and three-factor interactions in 2ⁿ and 3ⁿ plans. We also provide connected main effect plans for mixed level designs.     

On D-optimal robust designs for lifetime improvement experiments

Locating the optimal operating conditions of the process parameters is critical in a lifetime improvement experiment. For log-normal lifetime distribution with compound error structure (i.e., symmetry, inter-class and intra-class correlation error structures), we have developed methods for construction of D-optimal robust first order designs. It is shown that D-optimal robust first order designs are always robust first order rotatable but the converse is not always true.     

Constructions for point-regular linear spaces

We introduce the concept of simple difference family over a group G and relative to a partial spread in G. Such a family generates a point-regular linear space, i.e. a linear space with an automorphism group acting regularly on the point-set. In particular, we prove that any abelian linear space is generated by such a family. Using this new notion of difference family, we give a number of recursive constructions for point-regular linear spaces.     

Diffuse difference triangle sets

A particular kind of difference triangle sets (DTSs) called diffuse DTS (DDTS) are considered. Their combinatorial structure is underlying the construction of all known types of self-orthogonal diffuse codes. A number of constructions of DDTS are described, and lower and upper bounds on the maximal element of an optimal DDTS are given. The asymptotic behaviour of the maximal element is studied. Finally, tables of DDTS and of their minimal possible maximal elements are presented.     

Effect of choice complexity on design efficiency in conjoint choice experiments

Conjoint choice experiments have become a powerful tool to explore individual preferences. The consistency of respondents' choices depends on the choice complexity. For example, it is easier to make a choice between two alternatives with few attributes than between five alternatives with several attributes. In the latter case it will be much harder to choose the preferred alternative which is reflected in a higher response error. Several authors have dealt with this choice complexity in the estimation stage but very little attention has been paid to set up designs that take this complexity into account. The core issue of this paper is to find out whether it is worthwhile to take this complexity into account in the design stage. We construct efficient semi-Bayesian D-optimal designs for the heteroscedastic conditional logit model which is used to model the across respondent variability that occurs due to the choice complexity. The degree of complexity is measured by the entropy, as suggested by Swait and Adamowicz (2001). The proposed designs are compared with a semi-Bayesian D-optimal design constructed without taking the complexity into account. The simulation study shows that it is much better to take the choice complexity into account when constructing conjoint choice experiments.     

Control charts for attributes with maxima nominated samples

We develop quality control charts for attributes using the maxima nomination sampling (MNS) method and compare them with the usual control charts based on simple random sampling (SRS) method, using average run length (ARL) performance, the required sample size in detecting quality improvement, and non-existence region for control limits. We study the effect of the sample size, the set size, and nonconformity proportion on the performance of MNS control charts using ARL curve. We show that MNS control chart can be used as a better benchmark for indicating quality improvement or quality deterioration relative to its SRS counterpart. We consider MNS charts from a cost perspective. We also develop MNS attribute control charts using randomized tests. A computer program is designed to determine the optimal control limits for an MNS p-chart such that, assuming known parameter values, the absolute deviation between the ARL and a specific nominal value is minimized. We provide good approximations for the optimal MNS control limits using regression analysis. Theoretical results are augmented with numerical evaluations. These show that MNS based control charts can yield substantial improvement over the usual control charts based on SRS.     

Optimal paired comparison designs for first-order interactions

In many fields of applications paired comparisons are used in which either full or partial profiles of the alternatives are presented. For this situation we introduce an appropriate model and derive optimal designs in the presence of interactions when all attributes have the same number of levels.