onepl {lsirm12pl}

1PL Rasch model.

Description

onepl is used to fit 1PL Rasch model.

Usage

onepl(
  data,
  niter = 15000,
  nburn = 2500,
  nthin = 5,
  nprint = 500,
  jump_beta = 0.4,
  jump_theta = 1,
  pr_mean_beta = 0,
  pr_sd_beta = 1,
  pr_mean_theta = 0,
  pr_a_theta = 0.001,
  pr_b_theta = 0.001
)

Arguments

data

Matrix; binary item response matrix to be analyzed. Each row is assumed to be respondent and its column values are assumed to be response to the corresponding item.

niter

Numeric; number of iterations to run MCMC sampling. default value is 15000.

nburn

Numeric; number of initial, pre-thinning, MCMC iterations to discard. default value is 2500.

nthin

Numeric;number of thinning, MCMC iterations to discard. default value is 5.

nprint

Numeric; MCMC samples is displayed during execution of MCMC chain for each nprint. default value is 500.

jump_beta

Numeric; jumping rule of the proposal density for beta. default value is 0.4.

jump_theta

Numeric; jumping rule of the proposal density for theta. default value is 1.0.

pr_mean_beta

Numeric; mean of normal prior for beta. default value is 0.

pr_sd_beta

Numeric; standard deviation of normal prior for beta. default value is 1.0.

pr_mean_theta

Numeric; mean of normal prior for theta. default value is 0.

pr_a_theta

Numeric; shape parameter of inverse gamma prior for variance of theta. default value is 0.001.

pr_b_theta

Numeric; scale parameter of inverse gamma prior for variance of theta. default value is 0.001.

Details

onepl models the probability of correct response by respondent j to item i with item effect \beta_i, respondent effect \theta_j:

logit(P(Y_{j,i} = 1|\theta_j,\beta_i))=\theta_j+\beta_i

Value

onepl returns an object of list containing the following components:

beta_estimate

posterior estimation of beta.

theta_estimate

posterior estimation of theta.

sigma_theta_estimate

posterior estimation of standard deviation of theta.

beta

posterior samples of beta.

theta

posterior samples of theta.

theta_sd

posterior samples of standard deviation of theta.

accept_beta

accept ratio of beta.

accept_theta

accept ratio of theta.

Examples

# generate example item response matrix
data     <- matrix(rbinom(500, size = 1, prob = 0.5),ncol=10,nrow=50)

result <- onepl(data)