R: Fit a 2pl LSIRM for binary and continuous item resopnse data

lsirm2pl {lsirm12pl}

R Documentation

Fit a 2pl LSIRM for binary and continuous item resopnse data

Description

lsirm2pl integrates all functions related to 2PL LSIRM. Various 2PL 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

lsirm2pl(
  data,
  spikenslab = FALSE,
  fixed_gamma = FALSE,
  missing_data = NA,
  chains = 1,
  multicore = 1,
  seed = NA,
  ndim,
  niter,
  nburn,
  nthin,
  nprint,
  jump_beta,
  jump_theta,
  jump_alpha,
  jump_z,
  jump_w,
  pr_mean_beta,
  pr_sd_beta,
  pr_mean_theta,
  pr_a_theta,
  pr_b_theta,
  pr_mean_alpha,
  pr_sd_alpha,
  ...
)

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_alpha`	Numeric; the jumping rule for the alpha 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.
`pr_mean_alpha`	Numeric; the mean of the log normal prior for alpha. Default is 0.5.
`pr_sd_alpha`	Numeric; the standard deviation of the log normal prior for alpha. Default is 1.0.
`...`	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 2PL LSIRM with data included missing value are detailed in lsirm2pl_mar and lsirm2pl_mcar.

* For 2PL LSIRM using the spike-and-slab model selection approach are detailed in lsirm2pl_ss.

* For continuous version of 2PL LSIRM are detailed in lsirm2pl_normal_o.

For 2PL 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. 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,\alpha_i,\beta_i,\gamma,z_j,w_i))=\theta_j*\alpha_i+\beta_i-\gamma||z_j-w_i||

For 2PL 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. For 2pl model, the the item effect is assumed to have additional discrimination parameter \alpha_i multiplied by \theta_j:

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)

Value

lsirm2pl 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.
`alpha_estimate`	posterior estimates of alpha parameter..
`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.
`alpha`	Posterior samples of the alpha parameter.
`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.
`accept_alpha`	Acceptance ratio for the alpha parameter.
`...`	Additional return values for various settings. Refer to the functions in the Details.

Note

If both spikenslab and fixed_gamma are set TRUE, it returns error because both are related to gamma.

Examples


# generate example item response matrix
data     <- matrix(rbinom(500, size = 1, prob = 0.5),ncol=10,nrow=50)
lsirm_result <- lsirm2pl(data)

# The code following can achieve the same result.
lsirm_result <- lsirm(data~lsirm2pl())

[Package lsirm12pl version 1.3.2 Index]