R: Estimation of The Partial Credit Model with DIF

pcm_dif {autoRasch}

R Documentation

Estimation of The Partial Credit Model with DIF

Description

This function computes the parameter estimates of a partial credit model with DIF for dichotomous and polytomous responses by implementing the coordinate descent.

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

Usage

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

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

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

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

Arguments

`X`	A matrix or data frame as an input with ordinal responses (starting from 0); rows represent individuals, columns represent items.
`init_par`	a vector of initial values of the estimated parameters.
`groups_map`	Binary matrix. Respondents membership to DIF groups; rows represent individuals, column represent group partitions.
`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 `'pcmdif'`.
`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 `'pcmdif'`.
`...`	Further arguments to be passed.
`x`	The object of class `'pcmdif'`.

Value

pcm_dif() 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.

Examples

## Not run: 
pcmdif_res <- pcm_dif(shortDIF, groups_map = c(rep(1,50),rep(0,50)))
fit_res <- fitStats(pcmdif_res)
itemfit(fit_res)
personfit(fit_res)
plot_fitStats(fit_res, toPlot = c("alpha","outfit"), useName = FALSE)

## End(Not run)