By Marc Lavielle
''This booklet provides wide-ranging assurance of parametric modeling in linear and nonlinear mixed-effects versions. utilizing those versions, readers can practice parameter estimation throughout an entire inhabitants of people whilst. The booklet takes readers during the entire modeling procedure, from defining/creating a parametric version to appearing projects at the version utilizing a number of mathematical tools. It additionally includes a number of case experiences and illustrates using the MONOLIX software''--Provided via publisher. Read more...
summary: ''This ebook provides wide-ranging assurance of parametric modeling in linear and nonlinear mixed-effects versions. utilizing those versions, readers can practice parameter estimation throughout a complete inhabitants of people while. The ebook takes readers in the course of the entire modeling approach, from defining/creating a parametric version to appearing projects at the version utilizing quite a few mathematical tools. it's also a number of case reports and illustrates using the MONOLIX software''--Provided through writer
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Extra info for Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools
We show how to extend a proposed joint model for continuous outcomes to a joint model for continuous and categorical data. The last example then shows that mixed effects models can also be successfully used in quantitative biology for modeling the dynamics of biological networks in cell populations. Chapter 9 describes several algorithms useful for running tasks that interest us. In particular, the SAEM algorithm, used for estimating population parameters by maximum likelihood, is presented and its implementation described.
In other words, the model implementation is fully consistent with its mathematical representation. Furthermore, it is important to note that all of the tools we are going to use, for both modeling and simulation, are based on Mlxtran. , run several tasks based on the same model. 2 A declarative language allows variables to be defined using equations and definitions, rather than simply the calculation of their values. , “look at” what happens when we change the value of one or several parameters.
For nonlinear models, linearization or Monte Carlo methods can be used. 5 Optimal design In designing experiments for estimating statistical models, optimal design methods allow parameters to be estimated with minimum variance by optimizing some statistical criterion. Common optimality criteria are functionals of the eigenvalues of the expected Fisher information matrix def I ∗ (θ; u, t) = −Ey ∂2 log p(y; u, t, θ) . , a joint distribution py,ψ ( · ; θ, u, t) for (y, ψ). – a vector of population parameters θ.
Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools by Marc Lavielle