# Parameter Estimation Estimate paramters value by EM algorithm under the assumption of Sigmoid-Normal Model. ```r EMalgorithm(X, Y, Z, etat, alphat, sigmat, classsize = 2, learning_rate = 0.1, regular_parameter_eta = 0.001, max_iteration = 10000, max_iteration_eta = 10000, compact_flag = FALSE, C0 = 5, C1 = 2, C2 = 9) ``` ## Arguments - `X`: the covariables of the mean of each subgroup - `Y`: the respond variable - `Z`: the covaraibles determining subgroup - `etat`: the coeffients determining subgroup - `alphat`: the coeffients of the mean of each subgroup - `sigmat`: the variance of Y - `classsize`: the number of subgroup types in your model assumption - `learning_rate`: learning rate of updating eta - `regular_parameter_eta`: regular value of updating eta by gradiant descending methond. - `max_iteration`: maximum steps of interation to avoid unlimited looping. - `max_iteration_eta`: maximal steps of eta interation to avoid unlimited looping. - `compact_flag`: if the value of eta is limited in a compact set, set it TRUE - `C0`: the maximum of intercept of eta. - `C1`: the minimum of the norm of slope of eta - `C2`: the maximum of the norm of slope of eta ## Returns - **alpha**: alpha estimation - **eta**: eta estimation - **sigma**: sigma estimation ## Author(s) Linsui Deng ## Examples ```r #data generation samplesize <- 1000 classsize <- 2 etasize <- 3 alphasize <- 3 set.seed(1) Xtest <- data.frame(matrix(rnorm(samplesize*etasize),samplesize,etasize)) etatest <- matrix(c(1,2,-1, 0,0,0),etasize,classsize) Ztest <- matrix(rnorm(samplesize*alphasize),samplesize,alphasize) alphatest <- matrix(c(1,0,2, 5,0,7),alphasize,classsize) sigmatest <- 5 Wtest <- Wgenerate(alpha=alphatest,eta=etatest,X=Xtest,Z=Ztest,sigma=sigmatest) eta_initial <- matrix(c(rnorm(3),0,0,0),etasize,classsize) alpha_initial<- matrix(rnorm(alphasize*classsize)*3,alphasize,classsize) sigma_initial <- 1 EMtheta <- EMalgorithm(X=Wtest$X,Z=Wtest$Z,Y=Wtest$Y,classsize=2, etat=eta_initial,alphat=alpha_initial,sigmat=sigma_initial, learning_rate=0.01,regular_parameter_eta=0.001, max_iteration=1000,max_iteration_eta=10000, compact_flag = TRUE, C0 = 5, C1 = 2, C2 = 9) ```

EMalgorithm function