GPCMlasso {GPCMlasso}

GPCMlasso

Description

Performs GPCMlasso, a method to identify differential item functioning (DIF) in Generalized Partial Credit Models. A joint parametric model is set up based on an IRT model chosen by the user. Several variables can be considered simultaneously. For each pair between variable and item, a parametric DIF effect is introduced which indicates DIF if the respective parameter is selected (estimated to be unequal zero). Parameter selection is done using a lasso-type penalization term.

Usage

GPCMlasso(
  formula,
  data,
  DSF = FALSE,
  model = c("PCM", "RSM", "GPCM", "GRSM", "RM", "2PL"),
  control = ctrl_GPCMlasso(),
  cv = FALSE,
  main.effects = TRUE
)

Arguments

formula

Formula to indicate which items are considered and which covariates should be used to find DIF. Items are considered to be the response and are concatenated by cbind(). If the RHS of the formula is ~0, simply the model specified in model is calulated.

data

Data frame containing the ordinal item response data (as ordered factors) and all covariates.

DSF

Should Differential Step Functioning (DSF) be considered? If DSF = TRUE, one parameter per step between two response categories is introduced. For binary items, DSF and DIF conincide.

model

Specify the underlying basic model. Currently, you can choose between the partial credit model and the rating scale model and the respective generalized versions of both models called 'PCM', 'RSM', 'GPCM' and 'GRSM'. Generalized models allow for different discrimination parameters between items.

control

Control argument to specify further arguments for the algorithm and numerical optimization, specified by ctrl_GPCMlasso.

cv

Should cross-validation be performed? Cross-validation can be used as an alternative to BIC to select the optimal tuning parameter.

main.effects

Should also main effects of the variables be included in the model? Default is TRUE. Here, positive parameter estimates correspond to an increase of the respective trait if the variable increases.

Value

coefficients

Matrix containing all parameters for the GPCMlasso model, one row per tuning parameter lambda. Due to the penalty the parameters are scaled and, therefore, are comparable with respect to their size.

logLik

Vector of log-likelihoods, one value per tuning parameter lambda.

call

The function call of GPCMlasso

cv_error

Vector of cv_errors, one per tuning parameter. Only relevant if cv = TRUE.

model

Basic IRT model chosen by user.

data

Data from call.

control

Control list.

DSF

DSF from call.

formula

Formula from call.

item.names

Item names.

Y

Matrix containing item responses.

design_list

List containing several helpful objects for internal use.

AIC

Vector of AIC values, one per tuning parameter.

BIC

Vector of BIC values, one per tuning parameter.

cAIC

Vector of corrected AIC values, one per tuning parameter.

df

Vector of degrees of freedom, one per tuning parameter.

coef.rescal

Matrix containing all rescaled parameters for the GPCMlasso model, one row per tuning parameter lambda. In contrast to coefficients, all parameters are rescaled back to their original scales.

Author(s)

Gunther Schauberger
[e-mail]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

See Also

GPCMlasso-package, ctrl_GPCMlasso, print.GPCMlasso, plot.GPCMlasso, predict.GPCMlasso, trait.posterior

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)