IJPAM: Volume 36, No. 3 (2007)

ANALYZING MIXTURE EXPERIMENTS
VIA GENERALIZED LINEAR MODELS

Kadri Ulas Akay$^1$, Müjgân Tez$^2$
$^{1,2}$Department of Mathematics
Faculty of Arts and Sciences
University of Marmara
Göztepe-Kadiköy, Istanbul, 34722, TURKEY
$^1$e-mail: kadriulas@marmara.edu.tr
$^2$e-mail: mtez@marmara.edu.tr


Abstract.In the studies done till now, situations, where mixture experiments have a response with a normal distribution, have been taken into account. In case of having a response with a normal distribution, it would be sufficient to use Scheffé canonical polynomials and other mixture model forms for the analysis of the mixture experiments. However, as in many applications, there are situations when mixture experiments do not have a response with a normal distribution. In this paper, Generalized Linear Models (GLMs), which with a help of a link function takes advantage of natural distribution of the response, were used for the analysis of mixture experiments with a Gamma distribution. As a linear predictor, not only Scheffé models without a constant term were used but also mixture models with inverse terms were taken into account. The best subset models were obtained by using Gamma distribution together with canonical and non-canonical link functions. Then the proposed approach was examined on one example in literature.

Received: February 2, 2007

AMS Subject Classification: 62K99, 62J12

Key Words and Phrases: mixture experiments, generalized linear models, nonnormal response, Scheffé canonical polynomials, inverse terms in mixture models

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3