pcm_dif function

Estimation of The Partial Credit Model with DIF

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).

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'.

Returns

‘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.fitItem fit statistics.

• i.outfitMSQA vector of Outfit mean square values for each items.
• i.infitMSQA vector of Infit mean square values for each items.
• i.outfitZA vector of OutfitZ values for each items.
• i.infitZA vector of InfitZ values for each items.

p.fitPerson fit statistics.

• p.outfitMSQA vector of Outfit mean square values for each persons.
• p.infitMSQA vector of Infit mean square values for each persons.
• p.outfitZA vector of OutfitZ values for each persons.
• p.infitZA vector of InfitZ values for each persons.

traceMatSome computed matrices in the process.

• ematThe expected values matrix.
• vmatThe variance matrix.
• cmatThe curtosis matrix.
• std.resThe 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)

See Also

pcm, pcm_dif, gpcm, gpcm_dif