The equations for the estimation of the latent ability distribution and both item and latent distribution parameters under the multiple group framework using the two-parameter logistic model were presented in Chapter 10. In the present appendix, three procedures are implemented; estimation of latent distribution parameters assuming the item parameters are known, estimation of both item and latent distribution parameters for the compact model, and estimation of both item and latent distribution parameters for the augmented model. The estimation for the compact and augmented models illustrate an application of the multiple group model to the detection of differential item function.