pcm {autoRasch}

Estimation of The Partial Credit Model (PCM)

Description

This function computes the parameter estimates of a partial credit model for dichotomous and polytomous responses by using penalized joint maximum likelihood estimation (PJMLE). Inputting a dichotomous responses to this model, will automatically transforms the PCM to the Rasch model.

fitStats compute the fit statistics (e.g., Outfit and Infit) of the PCM model estimation (items and persons).

Usage

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

## S3 method for class 'pcm'
fitStats(obj, isAlpha = TRUE)

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

## S3 method for class 'pcm'
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.

obj

The object of class 'pcm'.

isAlpha

Boolean value that indicates whether the discrimination parameters is needed to be estimated or not. The discrimination parameters are estimated using the corresponding models (GPCM or GPCM-DIF).

object

The object of class 'pcm'.

...

Further arguments to be passed.

x

The object of class 'pcm'.

Value

pcm() will return a list which contains:

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.

beta

A vector of the difficulty parameter of each categories of items (thresholds).

theta

A vector of the ability parameters of each individuals.

fitStats() will return a list which contains:

alpha

A vector of estimated discrimination parameters for each items.

i.fit Item fit statistics.

• i.outfitMSQ A vector of Outfit mean square values for each items.

• i.infitMSQ A vector of Infit mean square values for each items.

• i.outfitZ A vector of OutfitZ values for each items.

• i.infitZ A vector of InfitZ values for each items.

p.fit Person fit statistics.

• p.outfitMSQ A vector of Outfit mean square values for each persons.

• p.infitMSQ A vector of Infit mean square values for each persons.

• p.outfitZ A vector of OutfitZ values for each persons.

• p.infitZ A vector of InfitZ values for each persons.

traceMat Some computed matrices in the process.

• emat The expected values matrix.

• vmat The variance matrix.

• cmat The curtosis matrix.

• std.res The standardized residual.

References

Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.

Masters, G. N. (1982). A rasch model for partial credit scoring. Psychometrika, 47(2), 149–174. https://doi.org/10.1007/BF02296272.

Wright, B. D., & Masters, G. N. (1990). Computation of outfit and infit statistics. Rasch Measurement Transactions, 3(4), 84–85. Retrieved from https://www.rasch.org/rmt/rmt34e.htm

See Also

pcm, gpcm

Examples

pcm_res <- pcm(shortDIF)
summary(pcm_res)

#To summarize only for beta parameters
summary(pcm_res, par="beta")
fit_res <- fitStats(pcm_res)
itemfit(fit_res)
personfit(fit_res)
plot_fitStats(fit_res, toPlot = c("alpha","outfit"), useName = TRUE)