EM Algorithms for DIF Detection in M2PL Models

Usage

D2PL_em(
  data,
  model = matrix(1, ncol(data)),
  group = rep(1, nrow(data)),
  method = "EMM",
  Lambda0 = if (length(unique(group)) == 1) 0 else seq(0.1, 1, by = 0.1),
  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)
model: A $J\times K$ binary matrix of loading indicators (all items load on the only dimension by default)
group: An $N$ dimensional vector of group indicators from 1 to G (all respondents are in the same group by default)
method: Estimation algorithm, one of 'EM' or 'EMM'
Lambda0: A vector of lambda0 values for $L_1$ penalty (lambda equals sqrt(N) * lambda0)
level: Accuracy level, either a number for mvQuad or a vector indicating the grid for each latent dimension
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) * lambda0
...$niter: Number(s) of iterations
...$Sigma: Group-level covariance matrices
...$Mu: Group-level mean vectors
...$a: Slopes for group 1
...$b: Intercepts for group 1
...$gamma: D2PL parameters for the slopes
...$beta: D2PL parameters for the intercepts
...$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_em(data, model, group))} # }

EM Algorithms for DIF Detection in M2PL Models

Usage

Arguments

Value

See also

Author

Examples