242 research outputs found
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 and missing data indicators , and
associated "missing at random"; (MAR) condition under which a model for
is unnecessary [Rubin, Biometrika 63 (1976) 581--592]. Most previous work has
treated and 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
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
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 PseudoâBayesian 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
On summary measures analysis of the linear mixed effects model for repeated measures when data are not missing completely at random
On summary measures analysis of the linear mixed effects model for repeated measures when data are not missing completely at random
Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation
Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight
into pathological and physiological alterations of living tissue, with the help
of which researchers hope to predict (local) therapeutic efficacy early and
determine optimal treatment schedule. However, the analysis of qMRI has been
limited to ad-hoc heuristic methods. Our research provides a powerful
statistical framework for image analysis and sheds light on future localized
adaptive treatment regimes tailored to the individual's response. We assume in
an imperfect world we only observe a blurred and noisy version of the
underlying pathological/physiological changes via qMRI, due to measurement
errors or unpredictable influences. We use a hidden Markov random field to
model the spatial dependence in the data and develop a maximum likelihood
approach via the Expectation--Maximization algorithm with stochastic variation.
An important improvement over previous work is the assessment of variability in
parameter estimation, which is the valid basis for statistical inference. More
importantly, we focus on the expected changes rather than image segmentation.
Our research has shown that the approach is powerful in both simulation studies
and on a real dataset, while quite robust in the presence of some model
assumption violations.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS157 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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