Midterm ProjectNames:Student IDs:1 Problem DescriptionRead article: Maximum Likelihood Algorithms for Generalized Linear Mixed Models (McCulloch1997), and try to understand the basic concept of generalized linear mixed model(GLMM). Section 3.1 in this paper described a Monte Carlo EM (MCEM) method to deriveMaximum Likelihood Estimates (MLE). Please use your own software (Matlab, R, C++,etc.) to perform following simulation study and answer related questions.1.1 Model and NotationsIn this project, we consider a clustering problem. Suppose we have observed n observations,each observation is a binary process, i.e. the response Yij = 0 or 1, i = 1, ..., n,j = 1, ..., T. Here n is the number of subjects and T is the length of observation. In general,T might vary across subjects, time points may also be different. In this project, however, wesimply assume that all subjects have common time length and time points. We also assumethat these subjects belong to two clusters. For each cluster, the conditional expectation of1response variable is:Pij ≡ E(Yij |Ui = 1, X1,ij , Z1,i) = g1(β1X1,ij + Z1,i)Pij ≡ E(Yij |Ui = 2, X2,ij , Z2,i) = g1(β2X2,ij + Z2,i) (1)where U is cluster membership, Xc,ij and Zc,i (c = 1, 2) are fixed and random effects,respectively. The link function g1（x) = exp(x)1+exp(x)is given. In a typical clustering problem, Uis usually unknown, and hence we treat U as another random effect.For random effects, we assume that Zc,i ～ N(0, σ2c) and P(U = 1) = π1 (then π2 =π1).Then the parameter to be estimated is .= {β1, β2, σ1, σ2, π1}. Treating random effects asmissing data, one can write the complete data likelihood function aswhere fc(Zc,i) is the density function of Normal distribution, fc(Yij |Zc,i) = Pωic is the dummy variable of Ui, i.e.�1 if subject i belongs to cluster c0 otherwise,1.2 Simulation Setup and RequirementGenerate 100 simulations. In each simulation, set n = 100 and T = 10. The true values ofparameter are: β1 = β2 = 1, π1 = 0.6,σ1 = 2, and σ2 = 10.Before you start, use N(0, 1) to generate the fixed effect X, and use them for all 100simulations. Please follow the paper mentioned earlier and use MCEM to evaluate the loglikelihoodfunction. In the E-step, perform K = 500 Gibbs sampling incorporated with aMetropolis-Hastings step, and drop the first 100 as a burn-in procedure.21.3 Your Report(1) Please write down the form of Monte Carlo average of log-likelihood (which you aregoing to evaluate)(2) Please write down details of the EM algorithm you use for this simulation, especiallythe Metropolis-Hastings steps.(3) What are your initial values? What is your convergence rule?(4) How to accelerate your EM algorithm? Any improvement you can observe?(4) Try different numbers of simulations: 200,300,...,1000. And plot the correspondingMSE.(5) Write a report in either Chinese or English. Please attach your code to your report.3本团队核心人员组成主要包括BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：99515681@qq.com 微信：codehelp QQ：99515681 或邮箱：99515681@qq.com 微信：codehelp
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