Model Selection Criteria for Missing-Data Problems Using the EM Algorithm

Abstract

We consider novel methods for the computation of model selection criteria in missing-data problems based on the output of the EM algorithm. The methodology is very general and can be applied to numerous situations involving incomplete data within an EM framework, from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and/or covariates. Toward this goal, we develop a class of information criteria for missing-data problems, called IC H,Q , which yields the Akaike information criterion and the Bayesian information criterion as special cases. The computation of IC H,Q requires an analytic approximation to a complicated function, called the H-function, along with output from the EM algorithm used in obtaining maximum likelihood estimates. The approximation to the H-function leads to a large class of information criteria, called IC H(k),Q . Theoretical properties of IC H(k),Q , including consistency, are investigated in detail. To eliminate the analytic approximation to the H-function, a computationally simpler approximation to IC H,Q , called IC Q , is proposed, the computation of which depends solely on the Q-function of the EM algorithm. Advantages and disadvantages of IC H(k),Q and IC Q are discussed and examined in detail in the context of missing-data problems. Extensive simulations are given to demonstrate the methodology and examine the small-sample and large-sample performance of IC H(k),Q and IC Q in missing-data problems. An AIDS data set also is presented to illustrate the proposed methodology.

Joint modeling of longitudinal drug using pattern and time to first relapse in cocaine dependence treatment data

“…A commonly used approach is to replace the log-likelihood with its conditional expectation given the observed data [Ibrahim, Zhu and Tang (2008)]. Hence, the AIC is of the form…”

Half-century archives of occupational medical data on French nuclear workers: a dusty warehouse or gold mine for epidemiological research?

“…A major limitation to the use of OM data for epidemiological research are the missing or incorrect values in the database. However, this issue can be addressed with frequentist (31) or Bayesian (32) or other methods (33). If there is no pattern to missing data, this could be resolved by careful data management, but if the errors are systematic, Bayesian method could help to fill them in.…”

The Fence Methods

“…The missing-data problem has a long history (e.g., Little and Rubin [28] [33], while model comparisons "demonstrate the effect of assumptions on estimates and tests, they do not indicate which modeling strategy is best, nor do they specifically address model selection for a given class of models. " The latter authors further proposed a class of model selection criteria based on the output of the E-M algorithm.…”

“…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.…”