A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models

Casero-Alonso, V., López-Fidalgo, J. and Torsney, B. (2017) A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models. Computer Methods and Programs in Biomedicine, 138, pp. 105-115. (doi: 10.1016/j.cmpb.2016.10.009) (PMID:27886709)

Abstract

Background and objective: Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. Methods: MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions. Results: The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Conclusions: Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights.

• Item Type: Articles
• Additional Information: Casero-Alonso and López-Fidalgo have been sponsored by Ministerio de Economía y Competitividad and fondos FEDER MTM2013-47879-C2-1-P and the Grant GI20163415 from UCLM.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Torsney, Dr Bernard
• Authors: Casero-Alonso, V., López-Fidalgo, J., and Torsney, B.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Computer Methods and Programs in Biomedicine
• Publisher: Elsevier
• ISSN: 0169-2607
• ISSN (Online): 1872-7565
• Published Online: 27 October 2016