lsirm1pl: Fit a 1PL LSIRM for binary and continuous item response data

Description

lsirm1pl integrates all functions related to 1PL LSIRM. Various 1PL LSIRM function can be used by setting the spikenslab, fixed_gamma, and missing_data arguments.

This function can be used regardless of the data type, providing a unified approach to model fitting.

Usage

lsirm1pl(
  data,
  spikenslab = FALSE,
  fixed_gamma = FALSE,
  missing_data = NA,
  chains = 1,
  multicore = 1,
  seed = NA,
  ndim = 2,
  niter = 15000,
  nburn = 2500,
  nthin = 5,
  nprint = 500,
  jump_beta = 0.4,
  jump_theta = 1,
  jump_z = 0.5,
  jump_w = 0.5,
  pr_mean_beta = 0,
  pr_sd_beta = 1,
  pr_mean_theta = 0,
  pr_a_theta = 0.001,
  pr_b_theta = 0.001,
  ...
)

Value

lsirm1pl returns an object of list. The basic return list containing the following components:

data: A data frame or matrix containing the variables used in the model.
bic: A numeric value representing the Bayesian Information Criterion (BIC).
mcmc_inf: Details about the number of MCMC iterations, burn-in periods, and thinning intervals.
map_inf: The log maximum a posteriori (MAP) value and the iteration number at which this MAP value occurs.
beta_estimate: Posterior estimates of the beta parameter.
theta_estimate: Posterior estimates of the theta parameter.
sigma_theta_estimate: Posterior estimates of the standard deviation of theta.
z_estimate: Posterior estimates of the z parameter.
w_estimate: Posterior estimates of the w parameter.
beta: Posterior samples of the beta parameter.
theta: Posterior samples of the theta parameter.
theta_sd: Posterior samples of the standard deviation of theta.
z: Posterior samples of the z parameter, represented as a 3-dimensional matrix where the last axis denotes the dimension of the latent space.
w: Posterior samples of the w parameter, represented as a 3-dimensional matrix where the last axis denotes the dimension of the latent space.
accept_beta: Acceptance ratio for the beta parameter.
accept_theta: Acceptance ratio for the theta parameter.
accept_z: Acceptance ratio for the z parameter.
accept_w: Acceptance ratio for the w parameter.
...: Additional return values for various settings. Refer to the functions in the Details.

Arguments

data: Matrix; a binary or continuous item response matrix for analysis. Each row represents a respondent, and each column contains responses to the corresponding item.
spikenslab: Logical; specifies whether to use a model selection approach. Default is FALSE.
fixed_gamma: Logical; indicates whether to fix gamma at 1. Default is FALSE.
missing_data: Character; the type of missing data assumed. Options are NA, "mar", or "mcar". Default is NA.
chains: Integer; the number of MCMC chains to run. Default is 1.
multicore: Integer; the number of cores to use for parallel execution. Default is 1.
seed: Integer; the seed number for MCMC fitting. Default is NA.
ndim: Integer; the dimension of the latent space. Default is 2.
niter: Integer; the total number of MCMC iterations to run. Default is 15000.
nburn: Integer; the number of initial MCMC iterations to discard as burn-in. Default is 2500.
nthin: Integer; the number of MCMC iterations to thin. Default is 5.
nprint: Integer; the interval at which MCMC samples are displayed during execution. Default is 500.
jump_beta: Numeric; the jumping rule for the beta proposal density. Default is 0.4.
jump_theta: Numeric; the jumping rule for the theta proposal density. Default is 1.0.
jump_z: Numeric; the jumping rule for the z proposal density. Default is 0.5.
jump_w: Numeric; the jumping rule for the w proposal density. Default is 0.5.
pr_mean_beta: Numeric; the mean of the normal prior for beta. Default is 0.
pr_sd_beta: Numeric; the standard deviation of the normal prior for beta. Default is 1.0.
pr_mean_theta: Numeric; the mean of the normal prior for theta. Default is 0.
pr_a_theta: Numeric; the shape parameter of the inverse gamma prior for the variance of theta. Default is 0.001.
pr_b_theta: Numeric; the scale parameter of the inverse gamma prior for the variance of theta. Default is 0.001.
...: Additional arguments for the for various settings. Refer to the functions in the Details.

Details

Additional arguments and return values for each function are documented in the respective function's description.

* For LSIRM with data included missing value are detailed in lsirm1pl_mar and lsirm1pl_mcar.

* For LSIRM using the spike-and-slab model selection approach are detailed in lsirm1pl_ss.

* For continuous version of LSIRM are detailed in lsirm1pl_normal_o.

For 1PL LSIRM with binary item response data, the probability of correct response by respondent $j$ to item $i$ with item effect $\beta_i$, respondent effect $\theta_j$ and the distance between latent position $w_i$ of item $i$ and latent position $z_j$ of respondent $j$ in the shared metric space, with $\gamma$ represents the weight of the distance term: $$logit(P(Y_{j,i} = 1|\theta_j,\beta_i,\gamma,z_j,w_i))=\theta_j+\beta_i-\gamma||z_j-w_i||$$

For 1PL LSIRM with continuous item response data, the continuous value of response by respondent $j$ to item $i$ with item effect $\beta_i$, respondent effect $\theta_j$ and the distance between latent position $w_i$ of item $i$ and latent position $z_j$ of respondent $j$ in the shared metric space, with $\gamma$ represents the weight of the distance term: $$Y_{j,i} = \theta_j+\beta_i-\gamma||z_j-w_i|| + e_{j,i}$$ where the error $e_{j,i} \sim N(0,\sigma^2)$.

Examples

Run this code

# \donttest{
# generate example item response matrix
data     <- matrix(rbinom(500, size = 1, prob = 0.5),ncol=10,nrow=50)
lsirm_result <- lsirm1pl(data)

# The code following can achieve the same result.
lsirm_result <- lsirm(data~lsirm1pl())

# }