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Simultaneous estimation of parameters in the bivariate Emax model
Author(s) -
Magnusdottir Bergrun T.,
Nyquist Hans
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6585
Subject(s) - bivariate analysis , inference , estimation , mathematics , statistics , estimation theory , bivariate data , variance (accounting) , statistical inference , econometrics , computer science , artificial intelligence , business , management , accounting , economics
In this paper, we explore inference in multi‐response, nonlinear models. By multi‐response, we mean models with m > 1 response variables and accordingly m relations. Each parameter/explanatory variable may appear in one or more of the relations. We study a system estimation approach for simultaneous computation and inference of the model and (co)variance parameters. For illustration, we fit a bivariate Emax model to diabetes dose‐response data. Further, the bivariate Emax model is used in a simulation study that compares the system estimation approach to equation‐by‐equation estimation. We conclude that overall, the system estimation approach performs better for the bivariate Emax model when there are dependencies among relations. The stronger the dependencies, the more we gain in precision by using system estimation rather than equation‐by‐equation estimation. Copyright © 2015 John Wiley & Sons, Ltd.