gpcm() R function from [autoRasch]

Estimation of The Generalized Partial Credit Model

This function computes the parameter estimates of a generalized partial credit model for polytomous responses by using penalized JML estimation. Inputting a dichotomous responses to this model, will automatically transforms the GPCM to the 2-PL model.


gpcm(X, init_par = c(), setting = c(), method = c("fast", "novel"))

## S3 method for class 'gpcm'
summary(object, ...)

## S3 method for class 'gpcm'
print(x, ...)

Arguments

X: Input dataset as matrix or data frame with ordinal responses (starting from 0); rows represent individuals, columns represent items.
init_par: a vector of initial values of the estimated parameters.
setting: a list of the optimization control setting parameters. See autoRaschOptions().
method: The implementation option of log likelihood function. fast using a c++ implementation and novel using an R implementation.
object: The object of class 'gpcm'.
...: Further arguments to be passed.
x: The object of class 'gpcm'.

Returns

X: The dataset that is used for estimation.
mt_vek: A vector of the highest response given to items.
itemName: The vector of names of items (columns) in the dataset.
loglik: The log likelihood of the estimation.
hessian: The hessian matrix. Only when the isHessian = TRUE.
gamma: A vector of the natural logarithm of discrimination parameters of each items.
beta: A vector of the difficulty parameter of each items' categories (thresholds).
theta: A vector of the ability parameters of each individuals.

Details

In the discrimination parameters estimation, instead of estimating the discrimination parameters ( $\alpha$ ), we are estimating its natural logarithm to avoid negative values, $\alpha = exp(\gamma)$ .

Examples


gpcm_res <- gpcm(short_poly_data)
summary(gpcm_res, par = "alpha")

References

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2). https://doi.org/10.1177/014662169201600206

gpcm function