DIFlasso: A Penalty Approach to Differential Item Functioning in Rasch...
In DIFlasso: A Penalty Approach to Differential Item Functioning in Rasch Models

Description Usage Arguments Details Value Author(s) References See Also Examples

A function to perform DIFlasso, a method to detect DIF (Differential Item Functioning) in Rasch Models. It can handle settings with many covariates and also metric covariates. The method is described in Tutz and Schauberger (2015).

1 2	DIFlasso(Y, X, l.lambda = 20, grouped = TRUE, trace = FALSE, df.type = c("YuanLin", "L2norm"))

`Y`	Data frame (one row per person, one column per item) containing response. May only contain 0 or 1.
`X`	Data frame (one row per person, one column per covariate) containing covariates. Has to be standardized.
`l.lambda`	Length of the grid of tuning parameters for DIFlasso. Default is 20 different tuning parameters.
`grouped`	Should all parameters corresponding to one item be grouped? If `grouped = FALSE`, ordinary Lasso instead of GroupLasso is performed.
`trace`	Should the trace of the `grplasso` function be printed?
`df.type`	Specifies the type of degrees of freedom. Default is to the definition of degrees of freedom by Yuan and Lin (2006). If `df.type = "L2norm"`, for every group (or parameter if `grouped = FALSE`), the ratio between the L2-norm of the penalized parameters and the parameters from the lowest tuning parameter is taken as degrees of freedom.

The method assumes the DIFmodel from Tutz and Schauberger (2015) where a Group Lasso penalty is used for DIF detection. Computation is based on the function grplasso.

`theta`	Estimated person abilities; one row per person, one column per tuning parameter
`beta`	Estimated item difficulties; one row per item, one column per tuning parameter
`gamma`	Estimated item-specific parameters; one row per item and covariate, one column per tuning parameter (first line: first item, first covariate; second line: first item, second covariate and so on)
`P`	Number of (valid) persons; removed persons are found in removed.persons
`I`	Number of items
`m`	Number of covariates
`logLik`	Log-likelihood
`BIC`	BIC
`AIC`	AIC
`df`	Degrees of freedom
`refit.matrix`	Design matrix for function `refitDIFlasso`
`lambda`	Sequence of tuning parameters used by `grplasso`
`ref.item`	Reference item
`dif.mat`	Estimates of the item-specific parameter estimates (at BIC-optimal lambda)
`dif.items`	Which items have been detected to be DIF items (at BIC-optimal lambda)?
`names.y`	Names of the items
`names.x`	Names of the covariates
`removed.persons`	Which persons have been removed because they either solved no item or all items?

Gunther Schauberger
gunther.schauberger@tum
https://www.sg.tum.de/epidemiologie/team/schauberger/

Tutz, Gerhard and Schauberger, Gunther (2015): A Penalty Approach to Differential Item Functioning in Rasch Models, Psychometrika, 80(1), 21 - 43

Yuan, Ming and Lin, Yi (2006): Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society B, 68(1), 49 - 67

refitDIFlasso, plot.DIFlasso, print.DIFlasso, grplasso

## Not run: 
data(simul.data)

Y <- simul.data[,1:10]
X <- simul.data[,11:13]

m1 <- DIFlasso(Y = Y, X = X, trace = TRUE) 
print(m1)
plot(m1)

m2 <- refitDIFlasso(m1)
print(m2)
plot(m2)

## End(Not run)