lsirmgrm_fixed_gamma is used to fit 1PL GRM LSIRM with gamma fixed to 1.
lsirmgrm_fixed_gamma(
data,
ncat = NULL,
missing_data = NA,
missing.val = 99,
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_sd_theta = 1,
pr_a_theta = 0.001,
pr_b_theta = 0.001,
adapt = NULL,
verbose = FALSE,
fix_theta_sd = FALSE
)lsirmgrm_fixed_gamma returns an object of list containing the same components as lsirmgrm.
Matrix; an ordinal (ordered categorical) item response matrix. Each row represents a respondent, and
each column represents an item. Values can be either 0:(K-1) or 1:K. Missing values can be NA.
Integer; number of categories \(K\). If NULL, it is inferred from the observed data.
Character; the type of missing data assumed. Options are NA, "mar", or
"mcar". If NA and data contains missing values, it is set to "mcar" internally.
Numeric; numeric code used to represent missing values in the C++ sampler. Default is 99.
Integer; number of MCMC chains. Default is 1.
Integer; number of cores for parallel execution when chains > 1. Default is 1.
Integer; RNG seed. Default is NA.
Integer; latent space dimension. Default is 2.
Integer; total MCMC iterations. Default is 15000.
Integer; burn-in iterations. Default is 2500.
Integer; thinning interval. Default is 5.
Integer; print interval if verbose=TRUE. Default is 500.
Numeric; proposal SD for GRM thresholds. Default is 0.4. During MCMC sampling, threshold proposals are constrained to maintain the ordering \(\beta_{i,1} > \beta_{i,2} > \cdots > \beta_{i,K-1}\) for each item.
Numeric; proposal SD for theta. Default is 1.
Numeric; proposal SD for z. Default is 0.5.
Numeric; proposal SD for w. Default is 0.5.
Numeric; prior mean for thresholds. Default is 0.
Numeric; prior SD for thresholds. Default is 1.
Numeric; prior mean for theta. Default is 0.
Numeric; prior SD for theta. Default is 1.
Numeric; shape for inverse-gamma prior on var(theta). Default is 0.001.
Numeric; scale for inverse-gamma prior on var(theta). Default is 0.001.
List; optional adaptive MCMC control. If not NULL, proposal standard deviations are adapted during the burn-in period to reach a target acceptance rate and are held fixed during the main MCMC sampling.
When adaptation is enabled, the reported acceptance ratios in the output (accept_beta, accept_theta, etc.) are computed only from iterations after burn-in, reflecting the performance of the adapted proposal distributions.
Elements of the list can include:
use_adapt: Logical; if TRUE, adaptive MCMC is used. Default is FALSE.
adapt_interval: Integer; the number of iterations between each update of the proposal SDs. Default is 100.
adapt_rate: Numeric; Robbins-Monro scaling constant (c) in step size formula: adapt_rate / iteration^decay_rate. Default is 1.0. Valid range: any positive value. Recommended: 0.5-2.0.
decay_rate: Numeric; Robbins-Monro decay exponent (alpha) in step size formula. Default is 0.5. Valid range: (0.5, 1]. Recommended: 0.5-0.8.
target_accept: Numeric; target acceptance rate for scalar parameters (beta, theta, gamma). Default is 0.44.
target_accept_zw: Numeric; target acceptance rate for latent positions z and w. Default is 0.234.
target_accept_beta/theta/gamma: Numeric; (optional) parameter-specific target acceptance rates to override target_accept.
Logical; If TRUE, MCMC samples are printed for each nprint. default value is FALSE
Logical; If TRUE, the standard deviation of the respondent latent positions \(\theta\) is fixed at 1 instead of being sampled. Default is FALSE.
# \donttest{
# generate example ordinal item response matrix
set.seed(123)
nsample <- 50
nitem <- 10
data <- matrix(sample(1:5, nsample * nitem, replace = TRUE), nrow = nsample)
# Fit 1PL GRM LSIRM with fixed gamma = 1
fit <- lsirmgrm_fixed_gamma(data, niter = 1000, nburn = 500)
summary(fit)
# }
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