Optimum mixture designs for the log-logistic dose–response model with mixture of two similar compounds
16 Mar 2018-Communications in Statistics - Simulation and Computation (Taylor & Francis)-Vol. 47, Iss: 3, pp 800-808
TL;DR: The aim is to investigate the D- and Ds-optimal mixture designs for the estimation of the full set of parameters or of potency for a best guess of the parameter values and to indicate how to find the optimal design to estimate the mixing proportions.
Abstract: The paper studies the log-logistic class of dose-response bioassay models in the binomial set-up. The dose is identified by the potency adjusted mixing proportions of two similar compounds. Models for both absence and presence of interaction between the compounds have been considered. The aim is to investigate the D- and Ds- optimal mixture designs for the estimation of the full set of parameters or for the estimation of potency for a best guess of the parameter values. We also indicate how to find the optimal design to estimate the mixing proportions at which the probability of success attains a given value in the absence of interaction effect.
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TL;DR: In this article, categorical data analysis was used for categorical classification of categorical categorical datasets.Categorical Data Analysis, categorical Data analysis, CDA, CPDA, CDSA
Abstract: categorical data analysis , categorical data analysis , کتابخانه مرکزی دانشگاه علوم پزشکی تهران
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01 Aug 1988
TL;DR: This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares.
Abstract: Wiley-Interscience Paperback Series The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models ...highly recommend[ed] ...for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." -Technometrics "[This book] provides a good balance of relevant theory and application with many examples ...[and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students." -Mathematical Reviews "[This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition ...[and is] a worthwhile reference for the marketing researcher with a serious interest in linear models. " -Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. The authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. The book also includes pseudocode for computing algorithms.
3,202 citations
"Optimum mixture designs for the log..." refers background in this paper
...Designs for logistic regression have been addressed at length in Finney (1978), Abdelbasit and Plackett (1983), andMeeker andHahn (1977)....
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...For nonlinear and binary logistic models, see also Agresti (2002, 2007), Bates and Watts (1988), Collett (2003), and Seber and Wild (1989)....
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TL;DR: In this article, the authors consider the problem of defining probability measures with finite support, i.e., measures that assign probability one to a set consisting of a finite number of points.
Abstract: Let f1 , …, fk be linearly independent real functions on a space X, such that the range R of (f1, …, fk) is a compact set in k dimensional Euclidean space. (This will happen, for example, if the fi are continuous and X is a compact topological space.) Let S be any Borel field of subsets of X which includes X and all sets which consist of a finite number of points, and let C = {e} be any class of probability measures on S which includes all probability measures with finite support (that is, which assign probability one to a set consisting of a finite number of points), and which are such that is defined. In all that follows we consider only probability measures e which are in C.
872 citations
"Optimum mixture designs for the log..." refers background in this paper
...The general Equivalence Theorem of Kiefer and Wolfowitz (1960) makes it possible to check the optimality of a continuous locally D-optimum design....
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TL;DR: This paper reviews the basic log-linear strategy and illustrates key concepts and Citations are given to other articles on these topics, many of which are nontechnical and contain substantive sociological applications.
Abstract: Log-linear methods provide a powerful framework and the statistical apparatus for rigorously analyzing categorical data. These methods were introduced and developed by Leo Goodman and others in the early 1970s. In the late 1970s and the early 1980s, Goodman, Alan Agresti, Clifford Clogg, Otis Dudley Duncan, and others showed how these models could help us to estimate associations between discrete variables, including ordered and unordered polytomies. The last decade has witnessed a set of diverse extensions of these techniques. This paper reviews the basic log-linear strategy and illustrates key concepts. Citations are given to other articles on these topics, many of which are nontechnical and contain substantive sociological applications.
305 citations
"Optimum mixture designs for the log..." refers background in this paper
...For nonlinear and binary logistic models, see also Agresti (2002, 2007), Bates and Watts (1988), Collett (2003), and Seber and Wild (1989)....
[...]
276 citations
"Optimum mixture designs for the log..." refers background in this paper
...The Equivalence Theorem states that for the optimal design ξ ∗, the maximum value of d(t, ξ ∗, θ) over the design space is equal to the number of parameters to be estimated, and this maximum value is attained at the support points of ξ ∗ (cf. Whittle, 1973)....
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