Estimate parameters with MCMC

estimate_thirt_params_mcmc(
  resp,
  items,
  control = list(),
  initial_params = list(),
  fixed_params = list(),
  op_params = list()
)

Arguments

resp: a data.frame of length [n_person x n_block] with at least three first variables: variable person of the format p for person number p, variable block of the format b for block number b, variable resp of the format r for response number r which corresponds to mupp::find_permutation_index().
items: a data.frame of length [total items] with five variables: variable item of the format i for item number i, variable block of the format b for block number b, variable dim of the format d for dimension number d, variable key with -1 for negatively- and 1 for positively-keyed items.
control: a list of three parameters to control the MCMC algorithm: n_iter for the number of iterations, n_burnin for the number of burn-ins, step_size_sd for the step size of new parameter generation, either one value for all 4 parameters, or a vector of 4 values in the following order: theta, gamma, lambda, psisq
initial_params: a list of initial parameters to start the algorithm, each parameter needs to be a matrix named theta, gamma, lambda, or psisq.
fixed_params: a list of fixed parameters to be excluded from estimation, each parameter needs to be a matrix named theta, gamma, lambda, or psisq.
op_params: a list of fixed parameters for operational items, each parameter needs to be a matrix named gamma, lambda, or psisq.

Value

a list of three objects if no operational items are provided: all_iters is a list of length [n_iter] for parameter estimates for all iterations, mean_mcmc is a list of length 4 for mean of four parameters after burn-ins, sd_mcmc is a list of length 4 for SD of four parameters after burn-ins. three additional objects are included if operational items are provided: all_iters_test includes all iterations for test items calibration, mean_mcmc_test includes parameter estimates for test items calibration, sd_mcmc_test includes parameter SD across iterations for test items calibration.

Examples

if (FALSE) {
set.seed(202108)

# designs
n_person      <- 100
n_item        <- 3
n_neg         <- 1
n_block       <- 2
n_dim         <- 4
n_iter        <- 1000
n_burnin      <- 20
step_size_sd  <- 0.1

# simulate parameters
params <- simulate_thirt_params(n_person = n_person,
                                n_item   = n_item,
                                n_neg    = n_neg,
                                n_block  = n_block,
                                n_dim    = n_dim)
resp   <- do.call(simulate_thirt_resp, params)
gamma  <- params$gamma$gamma
lambda <- params$items$lambda
psisq  <- params$items$psisq
theta  <- params$persons[, -1]

# operational parameters
op_gamma <- matrix(
  # first pair 1-2 is fixed for each of 2 blocks
  c(0.4, NA, NA,
   -0.9, NA, NA)
  )
op_lambda <- matrix(
  # first 2 items are fixed for each of 2 blocks
  c(-0.65, 0.55, NA,
    0.57, -0.40, NA)
  )
op_psisq <- matrix(
  # first 2 items are fixed for each of 2 blocks
  c(0.89, 0.72, NA,
    0.02, 0.41, NA)
)

# estimation output
start_mcmc <- Sys.time()
output     <- estimate_thirt_params_mcmc(resp  = resp$resp,
                                         items = resp$items,
                                         control = list(n_iter   = n_iter,
                                                        n_burnin = n_burnin,
                                                        step_size_sd = step_size_sd),
                                         op_params = list(gamma = op_gamma,
                                                          lambda = op_lambda,
                                                          psisq = op_psisq)
)
end_mcmc   <- Sys.time()

# correlate estimated and true parameters
diag(cor(theta, output$mean_mcmc$theta))
cor(gamma, output$mean_mcmc_test$gamma)
cor(lambda, output$mean_mcmc_test$lambda)
cor(psisq, output$mean_mcmc_test$psisq)
(time_mcmc <- end_mcmc - start_mcmc)
}