mirtjml_conf {mirtjml}

Constrained joint maximum likelihood estimation for confirmatory item factor analysis on the multidimensional two parameter logistic model.

Description

Constrained joint maximum likelihood estimation for confirmatory item factor analysis on the multidimensional two parameter logistic model.

Usage

mirtjml_conf(
  response,
  Q,
  theta0,
  A0,
  d0,
  cc = NULL,
  tol = 5,
  print_proc = TRUE
)

Arguments

response

N by J matrix containing 0/1/NA responses, where N is the number of respondents, J is the number of items, and NA indicates a missing response.

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.

theta0

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

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.

cc

A constant constraining the magnitude of the norms of person and item parameter vectors.

tol

The tolerance for convergence with a default value 5.

print_proc

Print the precision during the estimation procedure with a default value TRUE.

Value

The function returns a list with the following components:

theta_hat

The estimated person parameter matrix.

A_hat

The estimated loading parameter matrix

d_hat

The estimated intercept parameters.

References

Chen, Y., Li, X., & Zhang, S. (2019). Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications. Journal of the American Statistical Association <doi: 10.1080/01621459.2019.1635485>.

Examples

# load a simulated dataset
attach(data_sim)

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

# use all available cores by running
# setMIRTthreads(-1)

# run the confirmatory analysis
res_conf <- mirtjml_conf(response, Q, theta0, A0, d0)