montecarlo function

performs Monte Carlo simulations to generate empirical distributions

performs Monte Carlo simulations under no-DIF conditions to generate empirical distributions of statistics

montecarlo(obj, alpha = 0.01, nr = 100)

Arguments

• obj: an object returned from lordif
• alpha: desired significance level (e.g., .01)
• nr: number of replications

Details

Simulated datasets are generated under no-DIF conditions and have the same dimensions as the empirical dataset. Group n-sizes and differences (impact) in theta estimates are preserved in the simulated datasets. Returns empirical distributions and thresholds for various statistics and effect size measures.

Returns

Returns an object (list) of class "lordif.MC" with the following components: - call: calling expression

• chi12: prob associated with the LR Chi-square test comparing Model 1 vs. 2

• chi13: prob associated with the LR Chi-square test comparing Model 1 vs. 3

• chi23: prob associated with the LR Chi-square test comparing Model 2 vs. 3

• pseudo12.CoxSnell: Cox & Snell pseudo R-square change from Model 1 to 2

• pseudo13.CoxSnell: Cox & Snell pseudo R-square change from Model 1 to 3

• pseudo23.CoxSnell: Cox & Snell pseudo R-square change from Model 2 to 3

• pseudo12.Nagelkerke: Nagelkerke pseudo R-square change from Model 1 to 2

• pseudo13.Nagelkerke: Nagelkerke pseudo R-square change from Model 1 to 3

• pseudo23.Nagelkerke: Nagelkerke pseudo R-square change from Model 2 to 3

• pseudo12.McFadden: McFadden pseudo R-square change from Model 1 to 2

• pseudo13.McFadden: McFadden pseudo R-square change from Model 1 to 3

• pseudo23.McFadden: McFadden pseudo R-square change from Model 2 to 3

• beta12: proportional beta change from Model 1 to 2

• alpha: significance level

• nr: number of replications

• cutoff: thresholds for the statistics

References

Choi, S. W., Gibbons, L. E., Crane, P. K. (2011). lordif: An R Package for Detecting Differential Item Functioning Using Iterative Hybrid Ordinal Logistic Regression/Item Response Theory and Monte Carlo Simulations. Journal of Statistical Software, 39(8), 1-30. URL http://www.jstatsoft.org/v39/i08/.

Author(s)

Seung W. Choi choi.phd@gmail.com

Note

nr must be a large integer (e.g., 500) to generate smooth distributions.

See Also

permute, lordif

Examples

##load PROMIS Anxiety sample data (n=766)
## Not run: data(Anxiety)
##age : 0=younger than 65 or 1=65 or older
##run age-related DIF on all 29 items (takes about a minute)
## Not run: age.DIF <- lordif(Anxiety[paste("R",1:29,sep="")],Anxiety$age)
##the following takes several minutes
## Not run: age.DIF.MC <- montecarlo(age.DIF,alpha=0.01,nr=100)