regDIF {regDIF}

Regularized Differential Item Functioning

Description

Identify DIF in item response theory models using regularization.

Usage

regDIF(item.data,
       pred.data,
       prox.data = NULL,
       item.type = NULL,
       pen.type = NULL,
       pen.deriv = TRUE,
       tau = NULL,
       num.tau = 100,
       alpha = 1,
       gamma = 3,
       anchor = NULL,
       stdz = TRUE,
       control = list())

Arguments

item.data

Matrix or data frame of item responses. See below for supported item types.

pred.data

Matrix or data frame of predictors affecting item responses (DIF) and latent variable (impact). See control option below to specify different predictors for impact model.

prox.data

Optional vector of observed scores to serve as a proxy for the latent variable. If a vector is supplied, a multivariate regression model will be fit to the data. The default is NULL, indicating that latent scores will be estimated during model estimation.

item.type

Optional character value or vector indicating the type of item to be modeled. The default is NULL, corresponding to a 2PL or graded item type. Different item types may be specified for a single model by providing a vector equal in length to the number of items in item.data. The options include:

• "rasch" - Slopes constrained to 1 and intercepts freely estimated.

• "2pl" - Slopes and intercepts freely estimated.

• "graded" - Slopes, intercepts, and thresholds freely estimated.

• "cfa"

pen.type

Optional character value indicating the penalty function to use. The default is NULL, corresponding to the LASSO function. The options include:

• "lasso" - The least absolute selection and shrinkage operator (LASSO), which controls DIF selection through \tau (tau).

• "mcp" - The minimax concave penalty (MCP), which controls DIF selection through \tau (tau) and estimator bias through \gamma (gamma). Uses the firm-thresholding penalty function.

• "grp.lasso" - The group version of the LASSO penalty, which selects intercept and slope DIF effects on each background characteristic together.

• "grp.mcp" - The group version of the MCP function.

pen.deriv

Logical value indicating whether to use the second derivative of the penalized parameter during regularization. The default is TRUE.

tau

Optional numeric vector of tau values \ge 0. If tau is supplied, this overrides the automatic construction of tau values. Must be non-negative and in descending order, from largest to smallest values (e.g., seq(1,0,-.01).

num.tau

Numeric value indicating how many tau values to fit. The default is 100.

alpha

Numeric value indicating the alpha parameter in the elastic net penalty function. Alpha controls the degree to which LASSO or ridge is used during regularization. The default is 1, which is equivalent to LASSO. NOTE: If using MCP penalty, alpha may not be exactly 0.

gamma

Numeric value indicating the gamma parameter in the MCP function. Gamma controls the degree of tapering of DIF effects as tau decreases. Larger gamma leads to faster tapering (less bias but possibly more unstable optimization), whereas smaller gamma leads to slower tapering (more bias but more stable optimization). Default is 3. Must be greater than 1.

anchor

Optional numeric value or vector indicating which item response(s) are anchors (e.g., anchor = 1). Default is NULL, meaning at least one DIF effect per covariate will be fixed to zero as tau approaches 0 (required to identify the model).

stdz

Logical value indicating whether to standardize DIF and impact predictors for regularization. Default is TRUE, as it is recommended that all predictors be on the same scale.

control

Optional list of different model specifications and optimization parameters. May be:

impact.mean.data

Matrix or data frame of predictors, which allows for a different set of predictors to affect the mean impact equation compared to the item response DIF equations. Default includes all predictors from pred.data.

impact.var.data

Matrix or data frame with predictors for variance impact. See above. Default includes all predictors in pred.data.

tol

Convergence threshold of EM algorithm. Default is 10^-5.

maxit

Maximum number of EM iterations. Default is 2000.

adapt.quad

Logical value indicating whether to use adaptive quadrature to approximate the latent variable. The default is FALSE. NOTE: Adaptive quadrature is not supported yet.

num.quad

Numeric value indicating the number of quadrature points to be used. For fixed-point quadrature, the default is 21 points when all item responses are binary or else 51 points if at least one item is ordered categorical.

int.limits

Vector of 2 numeric values indicating the integral limits for quadrature. Default is c(-6,6).

optim.method

Character value indicating which optimization method to use. Default is "UNR", which updates estimates one-at-a-time using univariate Newton-Raphson, or a single iteration of coordinate descent. Another option is "MNR", which updates the impact and item parameter estimates using Multivariate Newton-Raphson. A third option is "CD", or coordinate descent with complete iterations through all parameters until convergence. "MNR" will be faster in most cases, although "UNR" may achieve faster results when the number of predictors is large.

start.values

List of numbers assigned as starting values to the regDIF procedure. List must contain only the following names: impact, for mean and variance impact parameters, in the order that is given by an object of class coef.regDIF; base, for base intercept and slope parameters, in order given by a coef.regDIF object; and finally, dif, for intercept and slope DIF parameters, again in order given by a coef.regDIF object.

Value

Function returns an object of class regDIF, which is a list of results from the regularization routine

Examples

library(regDIF)
head(ida)
item.data <- ida[,1:6]
pred.data <- ida[,7:9]
prox.data <- rowSums(item.data)
fit <- regDIF(item.data, pred.data, prox.data, num.tau = 10)
summary(fit)