Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups

The use of covariates in block designs is necessary when the covariates cannot be controlled like the blocking factor in the experiment. In this paper, we consider the situation where there is some flexibility for selection in the values of the covariates. The choice of values of the covariates for a given block design attaining minimum variance for estimation of each of the parameters has attracted attention in recent times. Optimum covariate designs in simple set-ups such as completely randomised design (CRD), randomised block design (RBD) and some series of balanced incomplete block design (BIBD) have already been considered. In this paper, optimum covariate designs have been considered for the more complex set-ups of different partially balanced incomplete block (PBIB) designs, which are popular among practitioners. The optimum covariate designs depend much on the methods of construction of the basic PBIB designs. Different combinatorial arrangements and tools such as orthogonal arrays, Hadamard matrices and different kinds of products of matrices viz. Khatri–Rao product, Kronecker product have been conveniently used to construct optimum covariate designs with as many covariates as possible.     

D-Optimal Designs for Covariate Models

The problem of finding D-optimal designs in the presence of a number of covariates has been considered in the one-way set-up. This is an extension of Dey and Mukerjee (2006 Dey , A. , Mukerjee , R. ( 2006 ). D-optimal designs for covariate models . Statistics 40 : 297 – 305 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) in the sense that for fixed replication numbers of each treatment, an alternative upper bound to the determinant of the information matrix has been found through completely symmetric C-matrices for the regression coefficients; this upper bound includes the upper bound given in Dey and Mukerjee (2006 Dey , A. , Mukerjee , R. ( 2006 ). D-optimal designs for covariate models . Statistics 40 : 297 – 305 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) obtained through diagonal C-matrices. Because of the fact that a smaller class of C-matrices was used at the intermediate stage where the replication numbers were fixed, ultimately some optimal designs remained unidentified there. These designs have been identified here and thereby the conjecture made in Dey and Mukerjee (2006 Dey , A. , Mukerjee , R. ( 2006 ). D-optimal designs for covariate models . Statistics 40 : 297 – 305 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) has been settled.     

Optimum designs for estimation of regression parameters in a balanced treatment incomplete block design set-up

The use of covariates in block designs is necessary when the experimental errors cannot be controlled using only the qualitative factors. The choice of values of the covariates for a given set-up attaining minimum variance for estimation of the regression parameters has attracted attention in recent times. In this paper, optimum covariate designs (OCD) have been considered for the set-up of the balanced treatment incomplete block (BTIB) designs, which form an important class of test-control designs. It is seen that the OCDs depend much on the methods of construction of the basic BTIB designs. The series of BTIB designs considered in this paper are mainly those as described by Bechhofer and Tamhane (1981) and Das et al. (2005). Different combinatorial arrangements and tools such as Hadamard matrices and different kinds of products of matrices viz Khatri-Rao product and Kronecker product have been conveniently used to construct OCDs with as many covariates as possible.     

The Impact of Community Context on Land Use in an Agricultural Society

As an initial step toward new models of the population-environment relationship, this paper explores the relationship between community context and local land use in an agricultural setting. In this type of setting, we argue that aspects of the community context, such as schools and transportation infrastructure, impact important environmental characteristics, such as land use. We provide hypotheses which explain the mechanisms producing these effects. We then use data from a study of 132 communities in rural Nepal to test our hypotheses. These analyses show that community characteristics are strongly associated with land use in this agricultural setting. The results point toward changes in communities as critical determinants of environmental quality. These findings are consistent with the notion that changes in community contexts may also condition the population-environment relationship.     

Nearly optimal covariate designs—Part I

We propose to discuss at length several examples from standard text books. All of these examples deal with analysis of covariance (ANCOVA) models and related analyses of data. We intend to capitalize on our understanding of optimal covariate designs (OCDs) in different ANCOVA models and re-visit these examples with a view to suggest optimal/nearly optimal designs for estimation of the covariate parameter(s). As we will see, for some examples our task is very much routine but for others, it is indeed a highly non trivial exercise.

?We intent to cover a total of six examples—divided in two parts. This is Part I—dealing with two examples.     

Optimal Descending Mechanisms for Constrained Procurement

Descending mechanisms for procurement (or, ascending mechanisms for selling) have been well‐recognized for their simplicity from the viewpoint of bidders—they require less bidder sophistication as compared to sealed‐bid mechanisms. In this study, we consider procurement under each of two types of constraints: (1) Individual/Group Capacities: limitations on the amounts that can be sourced from individual and/or subsets of suppliers, and (2) Business Rules: lower and upper bounds on the number of suppliers to source from, and on the amount that can be sourced from any single supplier. We analyze two procurement problems, one that incorporates individual/group capacities and another that incorporates business rules. In each problem, we consider a buyer who wants to procure a fixed quantity of a product from a set of suppliers, where each supplier is endowed with a privately known constant marginal cost. The buyer's objective is to minimize her total expected procurement cost. For both problems, we present descending auction mechanisms that are optimal mechanisms. We then show that these two problems belong to a larger class of mechanism design problems with constraints specified by polymatroids, for which we prove that optimal mechanisms can be implemented as descending mechanisms.     

Does Security Impact E‐procurement Performance? Testing a Model of Direct and Moderated Effects

Despite the widespread adoption of e‐procurement and the critical role of information security in these situations, academic research examining the relationship between information security and e‐procurement performance has been surprisingly minimal. This study represents an interdisciplinary approach to present and test a theoretical model that links security in e‐procurement processes to e‐procurement performance. E‐procurement performance is measured as a combination of cost savings, order quality, and satisfaction of fulfillment as perceived by buyers. The model also posits that two aspects of the procurement process will enhance the value of security in e‐procurement, namely, process complexity and process interdependence. We empirically examine these relationships using data collected from procurement managers. Our results have important implications for managing the e‐procurement process.     

D-Optimal Designs for Covariate Parameters in Block Design Set Up

The problem considered is that of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non stochastic controllable covariates, when N = 2(mod 4), N being the total number of observations. It is clear that when N ≠ 0 (mod 4), it is not possible to find designs attaining minimum variance for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters were established when each of the covariates belongs to the interval [?1, 1]. Some constructions of D-optimal design have been provided for symmetric balanced incomplete block design (SBIBD) with parameters b = v, r = k = v ? 1, λ =v ? 2 when k = 2 (mod 4) and b is an odd integer.     

Crossover design in clinical trials for binary response

In this paper, we consider a binary response model for the analysis of the two-treatment, two-period and four-sequence crossover design. We have introduced intra-patient drug dependency parameter in the model and provide two tests for the hypothesis of equality of treatment effects. We employ Monte Carlo simulation to compare our tests and a test that works under parallel design on the basis of type I error rate and power. We find that our procedures are dominant over the competitor with respect to power. Finally, we use a data set to illustrate the applicability of our procedure.