Showing papers by "Donald B. Rubin published in 1998"

Parameter expansion to accelerate EM: The PX-EM algorithm

Abstract: SUMMARY The EM algorithm and its extensions are popular tools for modal estimation but ar-e often criticised for their slow convergence. We propose a new method that can often make EM much faster. The intuitive idea is to use a 'covariance adjustment' to correct the analysis of the M step, capitalising on extra information captured in the imputed complete data. The way we accomplish this is by parameter expansion; we expand the complete-data model while preserving the observed-data model and use the expanded complete-data model to generate EM. This parameter-expanded Ei M, PX-EM, algorithm shares the simplicity and stability of ordinary EM, but has a faster rate of convergence since its M step performs a more efficient analysis. The PX-EM algorithm is illustrated for the multivariate t distribution, a random effects model, factor analysis, probit regression and a Poisson imaging model.

More powerful randomization-based p-values in double-blind trials with non-compliance.

Abstract: Standard randomization-based tests of sharp null hypotheses in randomized clinical trials, that is, intent-to-treat analyses, are valid without extraneous assumptions, but generally can be appropriately powerful only with alternative hypotheses that involve treatment assignment having an effect on outcome. In the context of clinical trials with non-compliance, other alternative hypotheses can be more natural. In particular, when a trial is double-blind, it is often reasonable for the alternative hypothesis to exclude any effect of treatment assignment on outcome for a unit unless the assignment affected which treatment that unit actually received. Bayesian analysis under this alternative 'exclusion' hypothesis leads to new estimates of the effect of receipt of treatment, and to a new randomization-based procedure that has frequentist validity yet can be substantially more powerful than the standard intent-to-treat procedure. The key idea is to obtain a p-value using a posterior predictive check distribution, which includes a model for non-compliance behaviour, although only under the standard sharp null hypothesis of no effect of assignment (or receipt) of treatment on outcome. It is important to note that these new procedures are distinctly different from 'as treated' and 'per protocol' analyses, which are not only badly biased in general, but generally have very low power.

Multiple imputation of missing blood alcohol concentration (bac) values in fars

Abstract: The National Highway Traffic Safety Administration (NHTSA) has undertaken several approaches to remedy the problem of missing blood alcohol test results in the Fatality Analysis Reporting System (FARS). The approach currently in use employs a linear discriminant model that estimates the probability that a driver or nonoccupant has a blood alcohol concentration (BAC) in grams per deciliter (g/dl) of 0.00, 0.01 to 0.09, or 0.10 and greater. The estimates are generated only for drivers and nonoccupants (pedestrians, pedalcyclists) for whom alcohol test results were not reported. The proposed methodology extends the current model by simulating specific values of BAC across the full range of possible values rather than estimating probabilities. By imputing ten values of BAC for each missing value, valid statistical inferences like variance, confidence intervals and deviation tests can be drawn. The estimation of discrete values also facilitates analysis by nonstandard boundaries of alcohol involvement (e.g., 0.08+).

Ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data

Abstract: SUMMARY The general location model (Olkin & Tate, 1961; Krzanowski, 1980, 1982; Little & Schluchter, 1985) has categorical variables marginally distributed as a multinomial and continuous variables conditionally normally distributed with different means across cells defined by the categorical variables but a common covariance matrix across cells Two extensions of the general location model are obtained The first replaces the common covariance matrix with different but proportional covariance matrices, where the proportionality constants are to be estimated The second replaces the multivariate normal distributions of the first extension with multivariate t distributions, where the degrees of freedom can also vary across cells and are to be estimated The t distribution is just one example of more general ellipsoidally symmetric distributions that can be used in place of the normal These extensions can provide more accurate fits to real data and can be viewed as tools for robust inference Moreover, the models can be very useful for multiple imputation of ignorable missing values Maximum likelihood estimation using the AECM algorithm (Meng & van Dyk, 1997) is presented, as is a monotone-data Gibbs sampling scheme for drawing parameters and missing values from their posterior distributions To illustrate the techniques, a numerical example is presented

A Broader Template for Analyzing Broken Randomized Experiments

Abstract: Randomized experiments suffering from missing data and noncompliance are a recurring problem for experimenters whose subjects are human. Until recently, analysts of such broken randomized experiments were largely forced to squeeze the data into the idealized template of the randomized experiment with neither noncompliance nor missing data. Such practices necessitate throwing away information and making strong, and often unwarranted, assumptions. The Milwaukee Parental Choice Program, a natural experiment, is used to illustrate the flexibility of a new template, which allows for missing data and certain forms of simple noncompliance. The generality of this new template, which is based on a formulation of causal effects called the Rubin causal model, is contrasted with existing alternatives. The multiple imputation technology needed to proceed with analyses from the framework of this template is briefly described, and technical aspects will be presented in depth in subsequent work.

Maximum likelihood estimation of factor analysis using the ecme algorithm with complete and incomplete data

Abstract: Factor analysis is a standard tool in educational testing contexts, which can be fit using the EM algorithm (Dempster, Laird and Rubin (1977)) An ex- tension of EM, called the ECME algorithm (Liu and Rubin (1994)), can be used to obtain ML estimates more efficiently in factor analysis models ECME has an E-step, identical to the E-step of EM, but instead of EM's M-step, it has a sequence of CM (conditional maximization) steps, each of which maximizes either the con- strained expected complete-data log-likelihood, as with the ECM algorithm (Meng and Rubin (1993)), or the constrained actual log-likelihood For factor analysis, we use two CM steps: the first maximizes the expected complete-data log-likelihood over the factor loadings given fixed uniquenesses, and the second maximizes the actual likelihood over the uniquenesses given fixed factor loadings We also de- scribe EM and ECME for ML estimation of factor analysis from incomplete data, which arise in applications of factor analysis in educational testing contexts ECME shares with EM its monotone increase in likelihood and stable convergence to an ML estimate, but converges more quickly than EM This more rapid convergence not only can shorten CPU time, but at least as important, it allows for a substan- tially easier assessment of convergence, as shown by examples We believe that the application of ECME to factor analysis illustrates the role that extended EM-type algorithms, such as the even more general AECM algorithm (Meng and van Dyk (1997)) and the PX-EM algorithm (Liu, Rubin and Wu (1997)), can play in fitting complex models that can arise in educational testing contexts

Combining Panel Data Sets with Attrition and Refreshment Samples

Abstract: In many fields researchers wish to consider statistical models that allow for more complex relationships than can be inferred using only cross-sectional data. Panel or longitudinal data where the same units are observed repeatedly at different points in time can often provide the richer data needed for such models. Although such data allows researchers to identify more complex models than cross-sectional data, missing data problems can be more severe in panels. In particular, even units who respond in initial waves of the panel may drop out in subsequent waves, so that the subsample with complete data for all waves of the panel can be less representative of the population than the original sample. Sometimes, in the hope of mitigating the effects of attrition without losing the advantages of panel data over cross-sections, panel data sets are augmented by replacing units who have dropped out with new units randomly sampled from the original population. Following Ridder (1992), who used these replacement units to test some models for attrition, we call such additional samples refreshment samples. We explore the benefits of these samples for estimating models of attrition. We describe the manner in which the presence of refreshment samples allows the researcher to test various models for attrition in panel data, including models based on the assumption that missing data are missing at random (MAR, Rubin, 1976; Little and Rubin, 1987). The main result in the paper makes precise the extent to which refreshment samples are informative about the attrition process; a class of non-ignorable missing data models can be identified without making strong distributional or functional form assumptions if refreshment samples are available.

Combining Panel Data Sets with Attrition and Refreshment Samples

Abstract: This discussion paper resulted in a publication in Econometrica (2001). Volume 69, issue 6, pages 1645-1659. With panel data important issues can be resolved that can not beaddressed with cross--sectional data. A major drawback is that paneldata suffer from more severe missing data problems. Adding a sampleconsisting of new units randomly drawn from the original populationas replacements for units who have dropped out of the panel, aso--called refreshment sample, can be helpful in mitigating theeffects of attrition, both by allowing for estimation of richermodels and by making estimation of conventional models moreprecise. In this paper we develop a family of models thatincorporate refreshment samples, and we demonstrate in an applicationto a Dutch data set on travel behaviour that such models can lead tosubstantially different results than models that assume that themissing data process is ignorable or conventional econometric modelsfor panel data with attrition.

Modeling schizophrenic behavior and testing drug efficacy using general mixture components

Abstract: A critical idea in the statistical analysis of randomized experiments is that the validity of the significance level for any test-statistic is assured by finding the randomization distribution of that statistic under the null hypothesis. Since validity under the null hypothesis is certain for any statistic, the most powerful statistic should be used to test for the equivalence of treatments, that is, the statistic that is most likely to detect true differences in the treatment conditions. We illustrate the critical points about validity and power using data from a randomized experiment comparing drugs for schizophrenic patients, where computing the scientific statistic requires extensive use of Markov chain Monte Carlo techniques to fit a model that reflects current understanding of components of schizophrenic behavior.