Comment: Struggles with Survey Weighting and Regression Modeling

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]Comment: Published in at http://dx.doi.org/10.1214/088342307000000186 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Block-Conditional Missing at Random Models for Missing Data

Two major ideas in the analysis of missing data are (a) the EM algorithm [Dempster, Laird and Rubin, J. Roy. Statist. Soc. Ser. B 39 (1977) 1--38] for maximum likelihood (ML) estimation, and (b) the formulation of models for the joint distribution of the data ${Z}$ and missing data indicators ${M}$, and associated "missing at random"; (MAR) condition under which a model for ${M}$ is unnecessary [Rubin, Biometrika 63 (1976) 581--592]. Most previous work has treated ${Z}$ and ${M}$ as single blocks, yielding selection or pattern-mixture models depending on how their joint distribution is factorized. This paper explores "block-sequential"; models that interleave subsets of the variables and their missing data indicators, and then make parameter restrictions based on assumptions in each block. These include models that are not MAR. We examine a subclass of block-sequential models we call block-conditional MAR (BCMAR) models, and an associated block-monotone reduced likelihood strategy that typically yields consistent estimates by selectively discarding some data. Alternatively, full ML estimation can often be achieved via the EM algorithm. We examine in some detail BCMAR models for the case of two multinomially distributed categorical variables, and a two block structure where the first block is categorical and the second block arises from a (possibly multivariate) exponential family distribution.Comment: Published in at http://dx.doi.org/10.1214/10-STS344 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Calibrated Bayes, for Statistics in General, and Missing Data in Particular

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are Bayesian, but frequentist methods are useful for model development and model checking. In this article the CB approach is outlined. Bayesian methods for missing data are then reviewed from a CB perspective. The basic theory of the Bayesian approach, and the closely related technique of multiple imputation, is described. Then applications of the Bayesian approach to normal models are described, both for monotone and nonmonotone missing data patterns. Sequential Regression Multivariate Imputation and Penalized Spline of Propensity Models are presented as two useful approaches for relaxing distributional assumptions.Comment: Published in at http://dx.doi.org/10.1214/10-STS318 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rejoinder

Rejoinder of "Calibrated Bayes, for Statistics in General, and Missing Data in Particular" by R. Little [arXiv:1108.1917]Comment: Published in at http://dx.doi.org/10.1214/10-STS318REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Turning marketing promises into business value: The experience of an industrial SME

The article studies the value that businesses should have for their customers and shareholders. It explains how to develop such value to meet or exceed customer's expectations through the application of the promise framework. The promise model includes promises made to customers, promises kept, and promises that involve a synchronized effort from the whole firm to create and deliver value to customers

Intention‐to‐treat analysis with treatment discontinuation and missing data in clinical trials

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112012/1/sim6352.pd

MISSING AT RANDOM AND IGNORABILITY FOR INFERENCES ABOUT SUBSETS OF PARAMETERS WITH MISSING DATA

For likelihood-based inferences from data with missing values, Rubin (1976) showed that the missing data mechanism can be ignored when (a) the missing data are missing at random (MAR), in the sense that missingness does not depend on the missing values after conditioning on the observed data, and (b) the parameters of the data model and the missing-data mechanism are distinct; that is, there are no a priori ties, via parameter space restrictions or prior distributions, between the parameters of the data model and the parameters of the model for the mechanism. Rubin described (a) and (b) as the weakest simple and general conditions under which it is always appropriate to ignore the process that causes missing data . However, these conditions are not always necessary. Also, they relate to the complete set of parameters in the model, but we argue that it would be useful to have definitions of MAR and ignorability for a subset of parameters of substantive interest. We propose such definitions, and apply them to a variety of examples where the missing data mechanism is missing not at random, but MAR or ignorable for the parameter subset

AN ANALYSIS OF NONIGNORABLE NONRESPONSE IN A SURVEY WITH A ROTATING PANEL DESIGN

Missing values to income questions are common in survey data. When the probabilities of nonresponse are assumed to depend on the observed information and not on the underlining unobserved amounts, the missing income values are missing at random (MAR), and methods such as sequential multiple imputation can be applied. However, the MAR assumption is often considered questionable in this context, since missingness of income is thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis based on a pattern-mixture model for deviations from MAR, in the context of missing income values in a rotating panel survey. The sensitivity analysis avoids the well-known problems of underidentification of parameters of non-MAR models, is easy to carry out using existing sequential multiple imputation software and has a number of novel features

A Pseudo‐Bayesian Shrinkage Approach to Regression with Missing Covariates

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93673/1/j.1541-0420.2011.01718.x.pd