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 gpcm
summary(object, ...)
# S3 method for gpcm
print(x, ...)
The dataset that is used for estimation.
A vector of the highest response given to items.
The vector of names of items (columns) in the dataset.
The log likelihood of the estimation.
The hessian matrix. Only when the isHessian = TRUE.
A vector of the natural logarithm of discrimination parameters of each items.
A vector of the difficulty parameter of each items' categories (thresholds).
A vector of the ability parameters of each individuals.
Input dataset as matrix or data frame with ordinal responses (starting from 0); rows represent individuals, columns represent items.
a vector of initial values of the estimated parameters.
a list of the optimization control setting parameters. See autoRaschOptions().
The implementation option of log likelihood function. fast using a c++ implementation and novel using an R implementation.
The object of class 'gpcm'.
Further arguments to be passed.
The object of class 'gpcm'.
In the discrimination parameters estimation, instead of estimating the discrimination parameters (\(\alpha\)), we are estimating its natural logarithm to avoid negative values, \(\alpha = exp(\gamma)\).
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)
summary(gpcm_res, par = "alpha")
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