gpcm {autoRasch} R Documentation

## Estimation of The Generalized Partial Credit Model

### Description

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.

### Usage

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'.

### 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).

### Value

 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.

### 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

pcm, gpcm
gpcm_res <- gpcm(short_poly_data)