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Application of Rstan package in parameter estimation of four-parameter logistic model. (Chinese. English summary) Zbl 1449.62167

Summary: The Stan program is a probabilistic programming language for estimating statistical models. Stan has a Cmdstan interface for the command line shell, a Pystan interface for Python, a Rstan interface for R, and a Matlabstan interface for Matlab. These interfaces can run on Windows, MacOSX, and Linux and are open sources licensed. The Rstan software package in the R software is mainly based on the two MCMC algorithms implemented by Rstan: HMC algorithm and the No-U-Turn sampler algorithm. The computational efficiency is better than Gibbs sampling and Metropolis algorithm. These two algorithms can be applied to any prior distribution. In this paper, firstly, the definition of four-parameter logistic model is introduced (that is, an upper asymptotic line less than 1 is added to the three-parameter logistic model, called the error parameter). Secondly, two MCMC algorithms with higher computational efficiency are introduced. We also introduce how to use the Rstan package to judge the convergence of the estimated model. Finally, the effectiveness and feasibility of the Rstan package in the four-parameter logistic model for parameter estimation are verified by simulation experiments.

MSC:

62J12 Generalized linear models (logistic models)
68N15 Theory of programming languages
62-08 Computational methods for problems pertaining to statistics
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