Showing papers by "Donald B. Rubin published in 1993"

Maximum likelihood estimation via the ECM algorithm: A general framework

Abstract: Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is computationally unattractive. In many cases, however, complete-data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

Identification of Causal Effects Using Instrumental Variables

Abstract: We outline a framework for causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the average causal effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat causal estimands with no interpretation as an average causal effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a...

Multiple imputation in mixture models for nonignorable nonresponse with follow-ups

Abstract: One approach to inference for means or linear regression parameters when the outcome is subject to nonignorable nonresponse is mixture modeling. Mixture models assume separate parameters for respondents and nonrespondents; implementation by multiple imputation consists of repeatedly filling in missing values for nonrespondents, estimating parameters using the filled-in data, and then adjusting for variability between imputations. We evaluated the performance of this scheme using simulated data with a 25% sample of nonrespondents followed up. We conclude that it provides a generally satisfactory and robust approach to inference for means and regression parameters in this case, although a greater number of imputations may be required for good performance compared to the number required for estimation when nonresponse is ignorable.

Identification of Causal Effects Using Instrumental Variables

Abstract: We outline a framework for causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the average causal effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat causal estimands with no interpretation as an average causal effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a...

Hierarchical logistic regression models for imputation of unresolved enumeration status in undercount estimation.

Abstract: In the process of collecting Post-Enumeration Survey (PES) data to evaluate census coverage, it is inevitable that there will be some individuals whose enumeration status (outcome in the census-PES match) remains unresolved even after extensive field follow-up operations. Earlier work developed a logistic regression framework for imputing the probability that unresolved individuals were enumerated in the census, so that the probability of having been enumerated is allowed to depend on covariates. The covariates may include demographic characteristics, geographic information, and census codes that summarize information on the characteristics of the match (e.g., the before-follow-up match code assigned by clerks to describe the type of match between PES and census records). In the production of 1990 undercount estimates, the basic logistic regression model was expanded into a mixed hierarchical model to allow for the presence of group-specific effects, where groups are characterized by common befor...

Tasks in statistical inference for studying variation in medicine.

Abstract: When studying variation in medicine, traditional hypothesis-testing procedures are too limited to obtain useful inferences except in special situations. More generally, full probability modelling is necessary. Even a relatively simple example can illustrate this point rather dramatically. The development and application of full-probability methods for medical problems comprise exciting areas for statistical and medical researchers, especially if working together.