Minimum cost linear trend-free 12-run fractional factorial designs

Time trend resistant fractional factorial experiments have often been based on regular fractionated designs where several algorithms exist for sequencing their runs in minimum number of factor-level changes (i.e. minimum cost) such that main effects and/or two-factor interactions are orthogonal to and free from aliasing with the time trend, which may be present in the sequentially generated responses. On the other hand, only one algorithm exists for sequencing runs of the more economical non-regular fractional factorial experiments, namely Angelopoulos et al. [1 P. Angelopoulos, H. Evangelaras, and C. Koukouvinos, Run orders for efficient two-level experimental plans with minimum factor level changes robust to time trends, J. Statist. Plann. Inference 139 (2009), pp. 3718–3724. doi: 10.1016/j.jspi.2009.05.002[Crossref], [Web of Science ®] , [Google Scholar]]. This research studies sequential factorial experimentation under non-regular fractionated designs and constructs a catalog of 8 minimum cost linear trend-free 12-run designs (of resolution III) in 4 up to 11 two-level factors by applying the interactions-main effects assignment technique of Cheng and Jacroux [3 C.S. Cheng and M. Jacroux, The construction of trend-free run orders of two-level factorial designs, J. Amer. Statist. Assoc. 83 (1988), pp. 1152–1158. doi: 10.1080/01621459.1988.10478713[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] on the standard 12-run Plackett–Burman design, where factor-level changes between runs are minimal and where main effects are orthogonal to the linear time trend. These eight 12-run designs are non-orthogonal but are more economical than the linear trend-free designs of Angelopoulos et al. [1 P. Angelopoulos, H. Evangelaras, and C. Koukouvinos, Run orders for efficient two-level experimental plans with minimum factor level changes robust to time trends, J. Statist. Plann. Inference 139 (2009), pp. 3718–3724. doi: 10.1016/j.jspi.2009.05.002[Crossref], [Web of Science ®] , [Google Scholar]], where they can accommodate larger number of two-level factors in smaller number of experimental runs. These non-regular designs are also more economical than many regular trend-free designs. The following will be provided for each proposed systematic design:

• (1) The run order in minimum number of factor-level changes.

• (2) The total number of factor-level changes between the 12 runs (i.e. the cost).

• (3) The closed-form least-squares contrast estimates for all main effects as well as their closed-form variance–covariance structure.

In addition, combined designs of each of these 8 designs that can be generated by either complete or partial foldover allow for the estimation of two-factor interactions involving one of the factors (i.e. the most influential).     

Selecting significant effects in factorial designs: Lenth’s method versus the Box-Meyer approach

The Lenth method is conceptually simple and probably the most common approach to analyzing the significance of the effects in factorial designs. Here, we compare it with a Bayesian approach proposed by Box and Meyer and which does not appear in the usual software packages. The comparison is made by simulating the results of 4, 8 and 16 run designs in a set of scenarios that mirror practical situations and analyzing the results provided by both methods. Although the results depend on the number of runs and the scenario considered, the use of the Box and Meyer method generally produces better results.     

Spillovers from targeting of incentives: Exploring responses to being excluded

A growing set of policies involve transfers conditioned upon socially desired actions, such as attending school or conserving forest. However, given a desire to maximize the impact of limited funds by avoiding transfers that do not change behavior, typically some potential recipients are excluded on the basis of their characteristics, their actions or at random. This paper uses a laboratory experiment to study the behavior of individuals excluded on different bases from a new incentive that encourages real monetary donations to a public environmental conservation program. We show that the donations from the individuals who were excluded based on prior high contributions fell significantly. Yet the rationale used for exclusion mattered, in that none of the other selection criteria used as the basis for exclusion resulted in negative effects on contributions.     

Estimating crop yield via Gaussian quadrature

The present study proposes a method to estimate the yield of a crop. The proposed Gaussian quadrature (GQ) method makes it possible to estimate the crop yield from a smaller subsample. Identification of plots and corresponding weights to be assigned to the yield of plots comprising a subsample is done with the help of information about the full sample on certain auxiliary variables relating to biometrical characteristics of the plant. Computational experience reveals that the proposed method leads to about 78% reduction in sample size with absolute percentage error of 2.7%. Performance of the proposed method has been compared with that of random sampling on the basis of the values of average absolute percentage error and standard deviation of yield estimates obtained from 40 samples of comparable size. Interestingly, average absolute percentage error as well as standard deviation is considerably smaller for the GQ estimates than for the random sample estimates. The proposed method is quite general and can be applied for other crops as well-provided information on auxiliary variables relating to yield contributing biometrical characteristics is available.     

The Law of Large Demand for Information

An unresolved problem in Bayesian decision theory is how to value and price information. This paper resolves both problems assuming inexpensive information. Building on Large Deviation Theory, we produce a generically complete asymptotic order on samples of i.i.d. signals in finite–state, finite–action models. Computing the marginal value of an additional signal, we find it is eventually exponentially falling in quantity, and higher for lower quality signals. We provide a precise formula for the information demand, valid at low prices: asymptotically a constant times the log price, and falling in the signal quality for a given price.     

Notes and Comments the Amsterdam Auction

The Amsterdam auction has been used to sell real estate in the Dutch capital for centuries. By awarding a premium to the highest losing bidder, the Amsterdam auction favors weak bidders without having the implementation difficulties of Myerson's (1981) optimal auction. In a series of experiments, we compare the standard first‐price and English auctions, the optimal auction, and two variants of the Amsterdam auction. With strongly asymmetric bidders, the second‐price Amsterdam auction raises substantially more revenues than standard formats and only slightly less than the optimal auction.     

Statistical Treatment Rules for Heterogeneous Populations

An important objective of empirical research on treatment response is to provide decision makers with information useful in choosing treatments. This paper studies minimax‐regret treatment choice using the sample data generated by a classical randomized experiment. Consider a utilitarian social planner who must choose among the feasible statistical treatment rules, these being functions that map the sample data and observed covariates of population members into a treatment allocation. If the planner knew the population distribution of treatment response, the optimal treatment rule would maximize mean welfare conditional on all observed covariates. The appropriate use of covariate information is a more subtle matter when only sample data on treatment response are available. I consider the class of conditional empirical success rules; that is, rules assigning persons to treatments that yield the best experimental outcomes conditional on alternative subsets of the observed covariates. I derive a closed‐form bound on the maximum regret of any such rule. Comparison of the bounds for rules that condition on smaller and larger subsets of the covariates yields sufficient sample sizes for productive use of covariate information. When the available sample size exceeds the sufficiency boundary, a planner can be certain that conditioning treatment choice on more covariates is preferable (in terms of minimax regret) to conditioning on fewer covariates.     

On choosing between fixed and random block effects in some no-interaction models

The purpose of this article is to strengthen the understanding of the relationship between a fixed-blocks and random-blocks analysis in models that do not include interactions between treatments and blocks. Treating the block effects as random has been recommended in the literature for balanced incomplete block designs (BIBD) because it results in smaller variances of treatment contrasts. This reduction in variance is large if the block-to-block variation relative to the total variation is small. However, this analysis is also more complicated because it results in a subjective interpretation of results if the block variance component is non-positive. The probability of a non-positive variance component is large precisely in those situations where a random-blocks analysis is useful – that is, when the block-to-block variation, relative to the total variation, is small. In contrast, the analysis in which the block effects are fixed is computationally simpler and less subjective. The loss in power for some BIBD with a fixed effects analysis is trivial. In such cases, we recommend treating the block effects as fixed. For response surface experiments designed in blocks, however, an opposite recommendation is made. When block effects are fixed, the variance of the estimated response surface is not uniquely estimated, and in practice this variance is obtained by ignoring the block effect. It is argued that a more reasonable approach is to treat the block effects to be random than to ignore it.     

Balanced Factorial Designs for cDNA Microarray Experiments

Balanced factorial designs are introduced for cDNA microarray experiments. Single replicate designs obtained using the classical method of confounding are shown to be particularly useful for deriving suitable balanced designs for cDNA microarrays. Classical factorial designs obtained using methods other than the method of confounding are also shown to be useful. The paper provides a systematic method of deriving designs for microarray experiments as opposed to algorithmic and ad-hoc methods and generalizes several of the microarray designs given recently in the literature.