EM Algorithm with ADMM for DIF Detection Using Group Pairwise Truncated $L_1$ Penalty in 2PL Models

Usage

D2PL_pair_em(
  data,
  group = rep(1, nrow(data)),
  Lambda0 = if (length(unique(group)) == 1) 0 else seq(0.5, 1.5, by = 0.1),
  Tau = if (length(unique(group)) == 1) 0 else c(Inf, seq(0.05, 0.3, by = 0.05)),
  rho0 = 0.5,
  level = 10,
  criterion = "BIC",
  iter = 200,
  eps = 0.001,
  c = 1,
  verbose = TRUE
)

Arguments

data: An $N\times J$ binary matrix of item responses (missing responses should be coded as NA)
group: An $N$ dimensional vector of group indicators from 1 to G (all respondents are in the same group by default)
Lambda0: A vector of lambda0 values for truncated $L_1$ penalty (lambda equals sqrt(N) / G * lambda0)
Tau: A vector of tau values for truncated $L_1$ penalty (becomes $L_1$ penalty when tau equals Inf)
rho0: A value of rho for augmented Lagrangian in ADMM (tau equals sqrt(N) / G * tau0)
level: Accuracy level of Gaussian quadrature for mvQuad
criterion: Information criterion for model selection, one of 'BIC' (recommended), 'AIC', or 'GIC'
iter: Maximum number of iterations
eps: Termination criterion on numerical accuracy
c: Constant for computing GIC
verbose: Whether to show the progress

Value

An object of class vemirt_DIF, which is a list containing the following elements:

N: Number of respondents
niter0: Number(s) of iterations for initialization
fit: The best (with lowest information criterion) model, which is an element of all
best: The index of fit in all
all: A list of models which has the same length as Lambda0:
...$lambda0: Corresponding element in Lambda0
...$lambda: sqrt(N) / G * lambda0
...$tau: Corresponding element in Tau
...$rho0: Same as rho0 in input
...$rho: sqrt(N) / G * rho0
...$niter: Number(s) of iterations
...$Sigma: Group-level covariance matrices
...$Mu: Group-level mean vectors
...$a: Slopes
...$b: Intercepts
...$d.a: Group pairwise differences of slopes
...$d.b: Group pairwise differences of intercepts
...$u.a: Lagrangian multipliers of corresponding elements in d.a
...$u.b: Lagrangian multipliers of corresponding elements in d.b
...$ll: Log-likelihood
...$l0: Number of nonzero D2PL parameters in gamma and beta
...$AIC: Akaike Information Criterion: -2*ll+l0*2
...$BIC: Bayesian Information Criterion: -2*ll+l0*log(N)
...$GIC: Generalized Information Criterion: -2*ll+c*l0*log(N)*log(log(N))

Author

Weicong Lyu <weiconglyu@um.edu.mo>

Examples

if (FALSE) { # \dontrun{
with(D2PL_data, D2PL_pair_em(data, group, Tau = c(Inf, seq(0.01, 0.05, by = 0.01))))} # }

EM Algorithm with ADMM for DIF Detection Using Group Pairwise Truncated \(L_1\) Penalty in 2PL Models

Usage

Arguments

Value

See also

Author

Examples