Catálogo de publicaciones - libros

Optimal designs for choice experiments with choice sets of size two are frequently derived under the assumption that all model parameters in a multinomial logit model are equal to zero. In this case, optimal designs for linear paired comparisons are also optimal for the choice model. It is shown that the methods for constructing linear paired comparison designs often require a considerably smaller number of choice sets when the parameters of primary interest are main effects.

In this paper locally D -optimal designs for the logistic regression model with two explanatory variables, both constrained to be greater than or equal to zero, and no interaction term are considered. The setting relates to dose-response experiments with doses, and not log doses, of two drugs. It is shown that there are two patterns of D -optimal design, one based on 3 and the other on 4 points of support, and that these depend on whether or not the intercept parameter β _0 is greater than or equal to a cut-off value of −1.5434. The global optimality of the designs over a range of β _0 values is demonstrated numerically and proved algebraically for the special case of the cut-off value of β _0.

In this paper experimental designs are considered for classic extreme value distribution models. A careful review of the literature provides some information matrices in order to study experimental designs. Regression models and their design implications are discussed for some situations involving extreme values. These include a constant variance and a constant coefficient of variation model plus an application in the context of strength of materials. Relative efficiencies calculated with respect to D-optimality are used to compare the designs given in this example.

Experiments with mixture and process variables are often constructed as the cross product of a mixture and a factorial design. Often it is not possible to implement all the runs of the cross product design, or the cross product model is too large to be of practical interest. We propose a methodology to select a model with a given number of terms and minimal condition number. The search methodology is based on weighted term orderings and can be extended to consider other statistical criteria.

The paper is devoted to experimental design for nonlinear regression models, whose derivatives with respect to parameters generate a generalized Chebyshev system. Most models of practical importance possess this property. In particular it is seen in exponential, rational and logistic models as well as splines with free knots. It is proved that support points of saturated locally D -optimal designs are monotonic and real analytic functions of initial values for those parameters on which models depend nonlinearly. This allows one to represent the functions by Taylor series. Similar properties of saturated maximin efficient designs are also investigated.

In this work, we consider an adaptive linear regression model designed to explain the patient’s response in a clinical trial. Patients are assumed to arrive sequentially. The adaptive nature of this statistical model allows the error terms to depend on the past which has not been permitted in other adaptive models in the literature. Some techniques of the theory of optimal designs are used in this framework to define new concepts: a-posteriori efficiency and mean a-posteriori efficiency . We then explicitly relate the variance of the allocation rule to the mean a-posteriori efficiency. These measures are useful for studying the comparative performance of adaptive designs. As an example, a comparative study is made among several design-adaptive designs to establish their properties with respect to a criterion of interest.

The paper briefly describes results on determining optimal cutpoints in a survey question. We focus on the case when we offer all respondents a set of cutpoints: a one point design. Applications in the social sciences will be cited, including contingent valuation studies, which aim to assess a population’s willingness to pay for some service or amenity, and in market research studies. The problem will be formulated as a generalized linear model. The formula for the Fisher information matrix is constructed. Search methods are used to find optimal solutions. Results are reported and illustrated pictorially.

This paper is concerned with the search for locally optimal designs when the observations of the response variable arise from a weighted distribution in an exponential family. The expression for the information matrices for length-biased distributions from an exponential family are obtained. Locally D -optimal designs are derived for regression models whose response variable follows a weighted Poisson distribution. Two link functions are considered for these models.

In the paper we present a method of calculating an efficient window design for parameter estimation in a non-linear mixed effects model. We define a window population design on the basis of a continuous design for such a model. The support points of the design belong to intervals whose boundaries are determined in a way which ensures that the efficiency of the design is high; also the width of the intervals is related to the dynamic system’s behaviour.

We consider optimal experimental design for parameter estimation in nonlinear situations where the optimal experiment depends on the value of the parameters to be estimated. Setting a prior distribution for these parameters, we construct criteria based on quantiles and probability levels of classical design criteria and show how their derivatives can easily be approximated, so that classical algorithms for local optimal design can be used for their optimisation.