Design Issues for Generalized Linear Models: A Review

Abstract

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal designs for 2k factorial experiments with binary response

“…The maximum likelihood estimator of β has an asymptotic covariance matrix (McCullagh and Nelder (1989); Khuri, Mukherjee, Sinha, and Ghosh (2006)) that is the inverse of nX ′ W X, where…”

“…Khuri, Mukherjee, Sinha, and Ghosh (2006) provided a systematic study of the optimal design problem in the GLM setup and recently there has been an upsurge in research in both theory and computation of optimal designs. Russell et al (2009), Majumdar (2008, 2009), Stufken (2009), Yang, Zhang, andHuang (2011), Stufken and Yang (2012) are some of the papers that developed theory, while Woods et al (2006), Steinberg (2006, 2008), Waterhouse et al (2008), Woods and van de Ven (2011) focused on developing efficient numerical techniques for obtaining optimal designs under generalized linear models.…”

An empirical comparison of some experimental designs for the valuation of large variable annuity portfolios

“…GLMs are usually used for data that do not satisfy the above assumptions. Unlike the case for linear models, there are not many design methods developed for GLMs due to the dependence problem that the design that minimizes the meansquared error of prediction depends on the unknown parameters [18]. Common approaches to addressing the dependence problem include:…”

Handling expensive optimization with large noise

“…algorithms without surrogate models, which tend to sample points close to the optimum. QLR is fully described by [12,8,21] (design of experiments for quadratic logistic model), [25] (active learning for logistic regression). See [10] for the code we used here, specifically tailored to binary noisy fitnesses.…”