The E-MS Algorithm: Model Selection With Incomplete Data

Abstract

We propose a procedure associated with the idea of the E-M algorithm for model selection in the presence of missing data. The idea extends the concept of parameters to include both the model and the parameters under the model, and thus allows the model to be part of the E-M iterations. We develop the procedure, known as the E-MS algorithm, under the assumption that the class of candidate models is finite. Some special cases of the procedure are considered, including E-MS with the generalized information criteria (GIC), and E-MS with the adaptive fence (AF; Jiang et al. 2008). We prove numerical convergence of the E-MS algorithm as well as consistency in model selection of the limiting model of the E-MS convergence, for E-MS with GIC and E-MS with AF. We study the impact on model selection of different missing data mechanisms. Furthermore, we carry out extensive simulation studies on the finite-sample performance of the E-MS with comparisons to other procedures. The methodology is also illustrated on a real data analysis involving QTL mapping for an agricultural study on barley grains.

Sumca: Simple, Unified, Monte-Carlo-assisted Approach to Second-Order Unbiased Mean-Squared Prediction Error Estimation

“…Following Jiang et al . (), in a PMS situation, the conditional expectations in model (2) are evaluated under , which is a true model, and , the vector of true parameters under , if the true parameters are given. With this understanding, all of the derivations in Section 2 carry through with ψ replaced by ψ f , and replaced by , the estimator of ψ f .…”

The Fence Methods

“…The idea is to combine the parameters with the model under which the parameters are defined, so that both the model and the parameters under the model are included in the E-M iteration. The convergence of E-MS as well as consistency has been established (Jiang et al [48]). Although the E-MS is not restricted to the fence, it would be interesting to compare it with the EMAF method, discussed in Section 6, in terms of performance in model selection with incomplete data.…”

“…The latter authors further proposed a class of model selection criteria based on the output of the E-M algorithm. Jiang et al [29] point out a potential drawback of the E-M approach of Ibrahim et al [33] in that the conditional expectation in the E-step is taken under the assumed (candidate) model, rather than an objective (true) model. Note that the complete-data log-likelihood is also based on the assumed model.…”

“…Although the E-MS is not restricted to the fence, it would be interesting to compare it with the EMAF method, discussed in Section 6, in terms of performance in model selection with incomplete data. Some initial comparison was made in Jiang et al [48] via a limited simulation study.…”

“…Jiang et al [48] proposed another method for model selection with incomplete data, known as the E-MS algorithm. The idea is to combine the parameters with the model under which the parameters are defined, so that both the model and the parameters under the model are included in the E-M iteration.…”