# ################################################################
# #                           Example 1                          #
# #             The GDI method to validate Q-matrix              #
# ################################################################
# set.seed(123)
# 
# library(Qval)
# 
# ## generate Q-matrix and data
# K <- 5
# I <- 20
# example.Q <- sim.Q(K, I)
# IQ <- list(
#   P0 = runif(I, 0.0, 0.2),
#   P1 = runif(I, 0.8, 1.0)
# )
# example.data <- sim.data(Q = example.Q, N = 500, IQ = IQ, model = "GDINA", distribute = "horder")
# 
# ## simulate random mis-specifications
# example.MQ <- sim.MQ(example.Q, 0.1)
# 
# ## using MMLE/EM to fit CDM model first
# example.CDM.obj <- CDM(example.data$dat, example.MQ)
# 
# ## using the fitted CDM.obj to avoid extra parameter estimation.
# Q.GDI.obj <- validation(example.data$dat, example.MQ, example.CDM.obj, method = "GDI")
# 
# 
# ## also can validate the Q-matrix directly
# Q.GDI.obj <- validation(example.data$dat, example.MQ)
# 
# ## item level iteration
# Q.GDI.obj <- validation(example.data$dat, example.MQ, method = "GDI", iter.level = "item", maxitr = 150)
# 
# ## search method
# Q.GDI.obj <- validation(example.data$dat, example.MQ, method = "GDI", search.method = "ESA")
# 
# ## cut-off point
# Q.GDI.obj <- validation(example.data$dat, example.MQ, method = "GDI", eps = 0.90)
# 
# ## check QRR
# print(zQRR(example.Q, Q.GDI.obj$Q.sug))
#