Stochastic GVEM for Confirmatory M3PL Analysis

Usage

C3PL_sgvem(
  u,
  indic,
  samp = 50,
  forgetrate = 0.51,
  mu_b,
  sigma2_b,
  Alpha,
  Beta,
  max.iter = 5000
)

Arguments

u: an \(N \times J\) matrix or a data.frame that consists of binary responses of \(N\) individuals to \(J\) items. The missing values are coded as NA
indic: a \(J \times K\) matrix or a data.frame that describes the factor loading structure of \(J\) items to \(K\) factors. It consists of binary values where 0 refers to the item is irrelevant with this factor, 1 otherwise
samp: a subsample for each iteration; default is 50
forgetrate: the forget rate for the stochastic algorithm. The value should be within the range from 0.5 to 1. Default is 0.51
mu_b: the mean parameter for the prior distribution of item difficulty parameters
sigma2_b: the variance parameter for the prior distribution of item difficulty parameters
Alpha: the \(\alpha\) parameter for the prior distribution of guessing parameters
Beta: the \(\beta\) parameter for the prior distribution of guessing parameters
max.iter: the maximum number of iterations for the EM cycle; default is 5000

Value

a list containing the following objects:

ra: item discrimination parameters, a \(J \times K\) matrix
rb: item difficulty parameters, vector of length \(J\)
rc: item guessing parameters, vector of length \(J\)
rs: variational parameters \(s\), a \(N \times J\) matrix
reta: variational parameters \(\eta(\xi)\), a \(N \times J\) matrix
reps: variational parameters \(\xi\), a \(N \times J\) matrix
rsigma: population variance-covariance matrix, 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
Q_mat: factor loading structure, a \(J \times K\) matrix
GIC: model fit index
AIC: model fit index
BIC: model fit index

References

Cho, A. E., Wang, C., Zhang, X., & Xu, G. (2021). Gaussian variational estimation for multidimensional item response theory. British Journal of Mathematical and Statistical Psychology, 74, 52-85.

Cho, A. E., Xiao, J., Wang, C., & Xu, G. (2022). Regularized Variational Estimation for Exploratory Item Factor Analysis. Psychometrika. https://doi.org/10.1007/s11336-022-09874-6

Author

Jiaying Xiao <jxiao6@uw.edu>

Examples

if (FALSE) { # \dontrun{
with(C3PL_data, C3PL_sgvem(data, model, samp=50, forgetrate=0.51, mu_b=0, sigma2_b=4, Alpha=10, Beta=40))} # }