GVEM Algorithms for DIF Detection in M1PL Models

Usage

D1PL_gvem(
  data,
  model = matrix(1, ncol(data)),
  group = rep(1, nrow(data)),
  a = 1,
  method = "IWGVEMM",
  Lambda0 = if (length(unique(group)) == 1) 0 else seq(0.1, 1, by = 0.1),
  criterion = "GIC",
  iter = 200,
  eps = 0.001,
  c = 1,
  S = 10,
  M = 10,
  lr = 0.1,
  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)
a: A scalar indicating the common discrimination parameter for all the dimensions of all the items (takes 1 by default)
method: Estimation algorithm, one of 'GVEM' or 'IWGVEMM'
Lambda0: A vector of lambda0 values for $L_1$ penalty (lambda equals sqrt(N) * lambda0)
criterion: Information criterion for model selection, one of 'GIC' (recommended), 'BIC', or 'AIC'
iter: Maximum number of iterations
eps: Termination criterion on numerical accuracy
c: Constant for computing GIC
S: Sample size for approximating the expected lower bound ('IWGVEMM' only)
M: Sample size for approximating a tighter lower bound ('IWGVEMM' only)
lr: Learning rate for the Adam optimizer ('IWGVEMM' only)
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: Person-level posterior covariance matrices
...$MU: Person-level posterior mean vectors
...$Sigma: Group-level covariance matrices
...$Mu: Group-level mean vectors
...$a: Slopes for group 1
...$b: Intercepts for group 1
...$gamma: D1PL parameters for the slopes (all elements are zero)
...$beta: D1PL parameters for the intercepts
...$RMSE: Root mean square error of fitted probability of each item for each group
...$ll: Estimated lower bound of log-likelihood
...$l0: Number of nonzero D1PL parameters in 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(D1PL_data, D1PL_gvem(data, model, group))} # }

GVEM Algorithms for DIF Detection in M1PL Models

Usage

Arguments

Value

See also

Author

Examples