UPCM (version 0.0-3)

UPCM: Uncertainty in (Generalized) Partial Credit Models

Description

Performs UPCM, a method to model uncertainty in (Generalized) Partial Credit Models

Usage

UPCM(
  Y,
  X = NULL,
  GPCM = TRUE,
  Q = 10,
  cores = 2,
  lambda = 0.01,
  se = TRUE,
  method = c("nlminb", "L-BFGS-B"),
  ctrl.nlminb = list(eval.max = 200, iter.max = 150, abs.tol = 1e-08, rel.tol = 1e-08,
    trace = 0, step.min = 0.1, x.tol = 1e-08, xf.tol = 1e-08)
)

Arguments

Y

Matrix containing the ordinal item response data (as ordered factors), one row per observation, one column per item.

X

Matrix containing explanatory variables which are used both for trait parameters and uncertainty parameters, one row per observation, one column per variable.

GPCM

Specifies the baseline model. GPCM = TRUE results in a UGPCM while GPCM = FALSE results in a UPCM.

Q

Number of nodes to be used (per dimension) in two-dimensional Gauss-Hermite-Quadrature.

cores

Number of cores to be used in parallelized computation

lambda

Tuning parameter for ridge penalty on all coefficients except sigma/slope parameters. Should be small, only used to stabilize results.

se

Should standard errors be computed? Standard errors are necessary for plot.UPCM. Computation is time-consuming because numerical optimization methods are used.

method

Specifies optimization algorithm used , either nlminb or L-BFGS-B (optim).

ctrl.nlminb

List of control arguments for optimization procedure nlminb.

Value

delta

Matrix containing all item parameters for the UPCM pr UGPCM model, one row per item, one column per category.

Sigma

2*2 covariance matrix for both random effects, namely the trait parameters theta and the uncertainty parameters alpha.

xi

Estimates for covariate effects on trait parameters.

alpha

Estimates for covariate effects on uncertainty parameters.

slopes

Estimates item slope parameters (only for GPCM = TRUE).

se.delta

se.xi

Estimates of standard errors for covariate effects on trait parameters.

se.alpha

Estimates of standard errors for covariate effects on uncertainty parameters.

se.sigma

Estimates of standard errors for covariance parameters. Attention: First and third parameter are estimates of se for both variances, the variance of theta and the variance of alpha. Second parameter is the estimate for correlation coefficient between theta and alpha, NOT of the corresponding covariance.

se.slopes

Estimates of standard errors of item slope parameters (only for GPCM = TRUE).

delta.GPCM

Estimates of item parameters theta in the PCM or GPCM model.

sigma.GPCM

Estimate of variance of trait parameters theta in the PCM or GPCM model.

slopes.GPCM

Estimates of slope parameters in the GPCM (only for GPCM = TRUE).

Y

Matrix containing the ordinal item response data, one row per obeservation, one column per item.

loglik

Marginal log-likelihood

coefs

Complete vector of all estimated parameters (for internal use).

se.vec

Complete vector of all estimated standard errors (for internal use).

References

Tutz, Gerhard and Schauberger, Gunther (2020): Uncertainty in Latent Trait Models, Applied Psychological Measurement, https://journals.sagepub.com/doi/abs/10.1177/0146621620920932?journalCode=apma

See Also

plot.UPCM UPCM-package

Examples

# NOT RUN {
data(tenseness)

Y <- data.matrix(tenseness[,1:4])
X <- model.matrix(~ Gender + Age, data = tenseness)[,-1]

m_upcm <- UPCM(Y = Y, X = X, cores = 2, GPCM = FALSE)
m_upcm
plot(m_upcm)
# }