StEM_mirt {lvmcomp}

Stochastic EM algorithm for solving multivariate item response theory model

Description

Stochastic EM algorithm for solving multivariate item response theory model

Usage

StEM_mirt(response, Q, A0, d0, theta0, sigma0, m = 200, TT = 20,
  max_attempt = 40, tol = 1.5, precision = 0.01, parallel = FALSE)

Arguments

response

N by J matrix containing 0/1 responses, where N is the number of respondents and J is the number of items.

Q

J by K matrix containing 0/1 entries, where J is the number of items and K is the number of latent traits. Each entry indicates whether an item measures a certain latent trait.

A0

J by K matrix, the initial value of loading matrix, satisfying the constraints given by Q.

d0

Length J vector, the initial value of intercept parameters.

theta0

N by K matrix, the initial value of latent traits for each respondent.

sigma0

K by K matrix, the initial value of correlations among the latent traits.

m

The length of Markov chain window for choosing burn-in size with a default value 200.

TT

The batch size with a default value 20.

max_attempt

The maximum number of batches before stopping.

tol

The tolerance of geweke statistic used for determining burn-in size with a default value 1.5.

precision

The precision value for determining the stopping of the algorithm with a default value 1e-2.

parallel

Whether or not enable the parallel computing with a default value FALSE.

Value

The function returns a list with the following components:

A_hat

The estimated loading matrix.

d_hat

The estimated value of intercept parameters.

sigma_hat

The estimated value of correlation matrix of latent traits.

burn_in_T

The length of burn-in size.

References

Zhang, S., Chen, Y. and Liu, Y. (2018). An Improved Stochastic EM Algorithm for Large-Scale Full-information Item Factor Analysis. British Journal of Mathematical and Statistical Psychology. To appear. D.C. Liu and J. Nocedal. On the Limited Memory Method for Large Scale Optimization (1989), Mathematical Programming B, 45, 3, pp. 503-528.

Examples

# run a toy example based on the M2PL model

# load a simulated dataset
attach(data_sim_mirt)

# generate starting values for the algorithm
A0 <- Q
d0 <- rep(0, J)
theta0 <- matrix(rnorm(N*K, 0, 1),N)
sigma0 <- diag(1, K) 

# do the confirmatory MIRT analysis
# to enable multicore processing, set parallel = T
mirt_res <- StEM_mirt(response, Q, A0, d0, theta0, sigma0)