Rstan包在四参数Logistic模型参数估计中的应用

Application of Rstan package in parameter estimation of four-parameter logistic model

Stan程序是一种用于估计统计模型的概率编程语言,Stan有命令行Shell的Cmdstan接口、Python的Pystan接口、R的Rstan接口、Matlab的Matlabstan接口,这些接口可以在Windows、MacOSX和Linux上运行,并且是开源许可的。R软件中Rstan软件包主要采用MCMC(Markov chain Monte Carlo)算法,并用来估计四参数Logistic模型(4PLM)。Rstan的实现主要2种MCMC算法:HMC算法和The No-U-Turn采样器算法,计算效率要优于Gibbs抽样和Metropolis算法,不仅如此,这2种算法适用于任何先验分布。首先,介绍了四参数Logistic模型的定义(即在三参数Logistic模型的基础上增加一条小于1的上渐进线,称为失误参数);其次,介绍了Rstan实现的2种计算效率更高的MCMC算法,还介绍了如何使用Rstan包判断估计参数收敛的方法;最后,通过模拟试验验证了Rstan包在四参数Logistic模型参数估计的有效性及可行性。

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 is open source 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 and Metropolis algorithm,not only that,these two algorithms apply to any prior distribution.Gibbsampling 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.It also introduces 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 parameter estimation are verified by simulation experiments.