twopl {lsirm12pl}

2PL Rasch model.

Description

twopl is used to fit 2PL Rasch model. Unlike 1PL model, 2PL model assumes the item effect can vary according to respondent, allowing additional parameter multiplied with respondent effect.

Usage

twopl(
  data,
  niter = 15000,
  nburn = 2500,
  nthin = 5,
  nprint = 500,
  jump_beta = 0.4,
  jump_theta = 1,
  jump_alpha = 1,
  pr_mean_beta = 0,
  pr_sd_beta = 1,
  pr_mean_theta = 0,
  pr_mean_alpha = 0.5,
  pr_sd_alpha = 1,
  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.

jump_alpha

Numeric; jumping rule of the proposal density for alpha 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_mean_alpha

Numeric; mean of normal prior for alpha. default value is 0.5.

pr_sd_alpha

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

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

twopl models the probability of correct response by respondent j to item i with item effect \beta_i, respondent effect \theta_j. For 2pl model, the the item effect is assumed to have additional discrimination parameter \alpha_i multiplied by \theta_j:

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

Value

twopl 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.

alpha_estimate

posterior estimation of alpha.

beta

posterior samples of beta.

theta

posterior samples of theta.

theta_sd

posterior samples of standard deviation of theta.

alpha

posterior samples of alpha.

accept_beta

accept ratio of beta.

accept_theta

accept ratio of theta.

accept_alpha

accept ratio of alpha.

Examples

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

result <- twopl(data)