Importance Weighted Version of GVEM Analysis for M2PL Models

An importance weighted version of GVEM (i.e., IW-GVEM) can be implemented to correct the bias on item parameters under M2PL models

Usage

C2PL_iw(u, gvem_result, S = 10, M = 10, max.iter = 10)

E2PL_iw(u, gvem_result, S = 10, M = 10, max.iter = 10)

Arguments

u

a \(N \times J\) matrix or a data.frame that consists of binary responses of \(N\) individuals to \(J\) items. The missing values are coded as NA

gvem_result

a list that includes exploratory or confirmatory GVEM results for M2PL models.

S

the number of times to draw samples;default is 10

M

the number of samples drawn from the variational distributions;default is 10

max.iter

the maximum number of iterations for the EM cycle; default is 10

Value

a list containing the following objects:

ra

item discrimination parameters estimated by GVEM, a \(J \times K\) matrix

rb

item difficulty parameters estimated by GVEM, vector of length \(J\)

reta

variational parameters \(\eta(\xi)\), a \(N \times J\) matrix

reps

variational parameters \(\xi\), a \(N \times J\) matrix

rsigma

population variance-covariance matrix estimated by GVEM, a \(K \times K\) matrix

mu_i

mean parameter for each person, a \(K \times N\) matrix

sig_i

covariance matrix for each person, a \(K \times K \times N\) array

n

the number of iterations for the EM cycle

rk

factor loadings, a \(J \times K\) matrix, for exploratory analysis only

Q_mat

factor loading structure, a \(J \times K\) matrix

GIC

model fit index

AIC

model fit index

BIC

model fit index

SE

Standard errors of item parameters, a \(J \times (K+1)\) matrix where the last column includes SE estimates for item difficulty parameters, for confirmatory analysis only

ur_a

item discrimination parameters before conducting the rotation, a \(J \times K\) matrix, for exploratory analysis only

new_a

item discrimination parameters estimated by IW-GVEM, a \(J \times K\) matrix

new_b

item difficulty parameters estimated by IW-GVEM, vector of length \(J\)

new_Sigma_theta

population variance-covariance matrix estimated by IW-GVEM, a \(K \times K\) matrix

best_lr

The learning rate used for importance sampling

best_lb

The lower bound value for importance sampling

See also

C2PL_gvem, E2PL_gvem_rot, C2PL_bs

Author

Jiaying Xiao <jxiao6@uw.edu>

Examples

if (FALSE) { # \dontrun{
CFA_result <- with(C2PL_data, C2PL_gvem(data, model))
C2PL_iw(C2PL_data$data, CFA_result)} # }
if (FALSE) { # \dontrun{
EFA_result <- with(E2PL_data_C1, E2PL_gvem_lasso(data, model, constrain = constrain, non_pen = non_pen))
E2PL_iw(E2PL_data_C1$data, EFA_result)} # }