StEM_pcirt {lvmcomp}

Stochastic EM algorithm for solving generalized partial credit model

Description

Stochastic EM algorithm for solving generalized partial credit model

Usage

StEM_pcirt(response, Q, A0, D0, theta0, sigma0, m = 200, TT = 20,
  max_attempt = 40, tol = 1.5, precision = 0.015, parallel = F)

Arguments

response

N by J matrix containing 0,1,...,M-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.

D0

J by M matrix containing the initial value of intercept parameters, where M is the number of response categories.

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 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 attampt times if the precision criterion is not meet.

tol

The tolerance of geweke statistic used for determining burn in size, default value is 1.5.

precision

The pre-set precision value for determining the length of Markov chain, default value is 0.015.

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 partial credit model

# load a simulated dataset
attach(data_sim_pcirt)

# generate starting values for the algorithm
A0 <- Q
D0 <- matrix(1, J, M)
D0[,1] <- 0
theta0 <- matrix(rnorm(N*K), N, K)
sigma0 <- diag(1, K)

# do the confirmatory partial credit model analysis 
# to enable multicore processing, set parallel = T
pcirt_res <- StEM_pcirt(response, Q, A0, D0, theta0, sigma0)