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## ----sim_setup, eval = F------------------------------------------------------
# ### Variables
# # Y = trial matix
# # C = KN vector of binary choices
# # N = #of subjects
# # J = # of items
# # K = # of choices
# # atrue = true item discriminations
# # btrue = true item locations
# # thetatrue = true thetas/latent performance
# # gamma = fixed effects coefficients
# # Sig = random-effects variance-covariance
# # subid = id variable for subjects
#
# # install mvtnorm is necessary
# # install.packages("mvtnorm")
#
# # Load the Library
# library(cIRT)
#
# # Simulate 2PNO Data
# N = 1000 # Students
# J = 20 # Total numbers of possible items per SA
#
# # Set a seed for the random generation of a's and b's.
# set.seed(1337)
#
# # Randomly pick a's and b's
#
# # Generate as, bs
# atrue=runif(J)+1
# btrue=2*runif(J)-1
#
# save(atrue, btrue, file="a_b_true.rda")
#
#
# # 2 Level Probit Data
# K = 30
#
# gam_notheta = c(.5,1)
# gam_theta = c(3,.25)
# gamma = c(gam_notheta,gam_theta)
#
# Sig = matrix(c(.25,0,0,.125),2,2)
#
# # Number of replications
# B = 100
#
# # Begin the Simulation Study
# for(b in 1:B){
#
# # Provide user with state information
# cat(paste0("On Iteration:",b,"\n"))
# set.seed(b + 1234)
#
# # True theta and etay
# thetatrue = rnorm(N)
# etay = outer(rep(1,N),atrue) * thetatrue - outer(rep(1,N),btrue)
#
# # Generate Y for 2PNO model
# p.correct = pnorm(etay)
# Y = matrix(rbinom(N*J, 1, p.correct),N,J)
#
# #################################################
# # Simulating 2 level probit data
# #################################################
#
# subid = expand.grid(cid = 1:K,sid = 1:N)[,2]
#
# pred = rnorm(K*N,0,1) # Pred
#
# center_pred = center_matrix(as.matrix(pred))
#
# Xnotheta = cbind(1,center_pred)
#
# Xtheta = rep(thetatrue,each=K)*Xnotheta
# X = cbind(Xnotheta,Xtheta)
#
#
# zetas = mvtnorm::rmvnorm(N,mean=c(0,0),sigma=Sig) # mvtnorm environment accessed
# W_veczeta = apply(Xnotheta*zetas[rep(1:N,each=K),],1,sum)
#
# etac = X%*%gamma + W_veczeta
# Zc = rnorm(N*K,mean=etac,sd=1)
# C = 1*(Zc>0)
#
# # Run the Choice Item Response Model
# out1 = cIRT(subid,
# Xnotheta,
# c(1,2),
# Xnotheta,
# Y,
# C,
# 5000)
#
# mname = paste0("model_",b)
#
# # Assign the data set name
# assign(mname, out1)
#
# # Save the out object
# save(list=mname, file=paste0(mname,".rda"))
#
# # Clean up Export
# rm(list = c(mname,"out1"))
# }
## ----sim_results, eval = F----------------------------------------------------
# # E[theta] - theta
# bias = function(theta.star, theta.true){
# matrix(mean(theta.star) - theta.true,ncol=1)
# }
#
# bias2 = function(theta.star, theta.true){
# matrix(theta.star - theta.true,ncol=1)
# }
#
# # sqrt ( 1/n * sum( (y_i - y.hat_i)^2 )
# RMSE = function(y,y.hat){
# sqrt( (y-y.hat)^2 )
# }
#
# # Change true values if needed
# # True Values
# gam_notheta = c(.5,1)
# gam_theta = c(3,.25)
# gamma = c(gam_notheta,gam_theta)
# # Loads a and b values
# load("a_b_true.rda")
#
# Sig = as.numeric(matrix(c(.25,0,0,.125),2,2))[c(1,2,4)]
# B = 100
#
# # Storage to hold bootstrap replications
# a_result = matrix(0, B, 20)
#
# b_result = matrix(0, B, 20)
#
# gs0_result = matrix(0, B, 2)
#
# beta_result = matrix(0, B, 2)
#
# sig_result = array(NA, dim=c(2,2,B))
#
#
# for(b in 1:B){
#
# mname = paste0("model_",b)
#
# load(paste0(mname, ".rda"))
#
# d = get(mname)
#
# a_result[i,] = apply(d$as, 2, FUN = mean)
# b_result[i,] = apply(d$bs, 2, FUN = mean)
#
# gs0_result[i,] = apply(d$gs0, 2, FUN = mean)
#
# beta_result[i,] = apply(d$betas, 2, FUN = mean)
#
# sig_result[,,i] = solve(apply(d$Sigma_zeta_inv, c(1,2), FUN = mean))
# }
#
# # Obtain an overall mean for each of the following:
#
# m_a_result = apply(a_result, 2, FUN = mean)
#
# m_b_result = apply(b_result, 2, FUN = mean)
#
# m_gs0_result = apply(gs0_result, 2, FUN = mean)
#
# m_beta_result = apply(beta_result, 2, FUN = mean)
#
# m_sig_result = as.numeric(apply(sig_result, c(1,2), FUN = mean))[c(1,2,4)]
#
#
# # Perform a bias evaluation given the true values:
#
# a_bias = bias2(m_a_result,atrue)
#
# b_bias = bias2(m_b_result,btrue)
#
# gs0_bias = bias2(m_gs0_result,gamma[1:2])
#
# beta_bias = bias2(m_beta_result,gamma[3:4])
#
# sig_bias = bias2(m_sig_result, Sig)
#
# # Perform the RMSE under the supplied results:
#
# a_RMSE = RMSE(m_a_result,atrue)
#
# b_RMSE = RMSE(m_b_result,btrue)
#
# gs0_RMSE = RMSE(m_gs0_result,gamma[1:2])
#
# beta_RMSE = RMSE(m_beta_result,gamma[3:4])
#
# sig_RMSE = RMSE(m_sig_result, Sig)
## ----out, eval = F------------------------------------------------------------
# # Make a results export
# results_a = cbind(m_a_result, atrue, a_bias, a_RMSE)
#
# rownames(results_a) = paste0("Item ",1:length(atrue))
#
# colnames(results_a) = c("$a$ Estimate", "$a$ True", "$a$ Bias", "$a$ RMSE")
#
# results_b = cbind(m_b_result, btrue, b_bias, b_RMSE)
#
# rownames(results_b) = paste0("Item ",1:length(btrue))
# colnames(results_b) = c("$b$ Estimate", "$b$ True", "$b$ Bias", "$b$ RMSE")
#
# results_gs0 = cbind(m_gs0_result,gamma[1:2],gs0_bias,gs0_RMSE)
# rownames(results_gs0) = paste0("$\\gamma_",1:2,"$")
# colnames(results_gs0) = c("$\\beta$ Estimate", "$\\beta$ True", "$\\beta$ Bias", "$\\beta$ RMSE")
#
# results_beta = cbind(m_beta_result,gamma[3:4],beta_bias,beta_RMSE)
# rownames(results_beta) = paste0("$\\beta_",1:2,"$")
# colnames(results_beta) = c("$\\beta$ Estimate", "$\\beta$ True", "$\\beta$ Bias", "$\\beta$ RMSE")
#
# results_sig_zeta = cbind(m_sig_result,Sig,sig_bias,sig_RMSE)
# rownames(results_sig_zeta) = c("$\\Zeta_{1,1}$","$\\Zeta_{2,1} = $\\Zeta_{1,2}$", "$\\Zeta_{2,2}$")
# colnames(results_sig_zeta) = c("$\\Sigma_{\\Zeta}$ Estimate", "$\\beta$ True", "$\\beta$ Bias", "$\\beta$ RMSE")
#
# save(results_a, results_b, results_gs0, results_beta, results_sig_zeta, file="sim_results.rda")
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