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Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit

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Zeitschriftentitel: Journal of the Royal Statistical Society Series B: Statistical Methodology
Personen und Körperschaften: Molenberghs, Geert, Beunckens, Caroline, Sotto, Cristina, Kenward, Michael G.
In: Journal of the Royal Statistical Society Series B: Statistical Methodology, 70, 2008, 2, S. 371-388
Medientyp: E-Article
Sprache: Englisch
veröffentlicht:
Oxford University Press (OUP)
Schlagwörter:
author_facet Molenberghs, Geert
Beunckens, Caroline
Sotto, Cristina
Kenward, Michael G.
Molenberghs, Geert
Beunckens, Caroline
Sotto, Cristina
Kenward, Michael G.
author Molenberghs, Geert
Beunckens, Caroline
Sotto, Cristina
Kenward, Michael G.
spellingShingle Molenberghs, Geert
Beunckens, Caroline
Sotto, Cristina
Kenward, Michael G.
Journal of the Royal Statistical Society Series B: Statistical Methodology
Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
Statistics, Probability and Uncertainty
Statistics and Probability
author_sort molenberghs, geert
spelling Molenberghs, Geert Beunckens, Caroline Sotto, Cristina Kenward, Michael G. 1369-7412 1467-9868 Oxford University Press (OUP) Statistics, Probability and Uncertainty Statistics and Probability http://dx.doi.org/10.1111/j.1467-9868.2007.00640.x <jats:title>Summary</jats:title><jats:p>Over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed, many of which allowing for the missingness to be not at random, in the sense that the unobserved measurements influence the process governing missingness, in addition to influences coming from observed measurements and/or covariates. The fundamental problems that are implied by such models, to which we refer as sensitivity to unverifiable modelling assumptions, has, in turn, sparked off various strands of research in what is now termed sensitivity analysis. The nature of sensitivity originates from the fact that a missingness not at random (MNAR) model is not fully verifiable from the data, rendering the empirical distinction between MNAR and missingness at random (MAR), where only covariates and observed outcomes influence missingness, difficult or even impossible, unless we are willing to accept the posited MNAR model in an unquestioning way. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Of course, such a pair of models will produce different predictions of the unobserved outcomes, given the observed outcomes. Theoretical considerations are supplemented with an illustration that is based on the Slovenian public opinion survey, which has been analysed before in the context of sensitivity analysis.</jats:p> Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit Journal of the Royal Statistical Society Series B: Statistical Methodology
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title Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_unstemmed Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_full Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_fullStr Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_full_unstemmed Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_short Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_sort every missingness not at random model has a missingness at random counterpart with equal fit
topic Statistics, Probability and Uncertainty
Statistics and Probability
url http://dx.doi.org/10.1111/j.1467-9868.2007.00640.x
publishDate 2008
physical 371-388
description <jats:title>Summary</jats:title><jats:p>Over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed, many of which allowing for the missingness to be not at random, in the sense that the unobserved measurements influence the process governing missingness, in addition to influences coming from observed measurements and/or covariates. The fundamental problems that are implied by such models, to which we refer as sensitivity to unverifiable modelling assumptions, has, in turn, sparked off various strands of research in what is now termed sensitivity analysis. The nature of sensitivity originates from the fact that a missingness not at random (MNAR) model is not fully verifiable from the data, rendering the empirical distinction between MNAR and missingness at random (MAR), where only covariates and observed outcomes influence missingness, difficult or even impossible, unless we are willing to accept the posited MNAR model in an unquestioning way. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Of course, such a pair of models will produce different predictions of the unobserved outcomes, given the observed outcomes. Theoretical considerations are supplemented with an illustration that is based on the Slovenian public opinion survey, which has been analysed before in the context of sensitivity analysis.</jats:p>
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author Molenberghs, Geert, Beunckens, Caroline, Sotto, Cristina, Kenward, Michael G.
author_facet Molenberghs, Geert, Beunckens, Caroline, Sotto, Cristina, Kenward, Michael G., Molenberghs, Geert, Beunckens, Caroline, Sotto, Cristina, Kenward, Michael G.
author_sort molenberghs, geert
container_issue 2
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container_title Journal of the Royal Statistical Society Series B: Statistical Methodology
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description <jats:title>Summary</jats:title><jats:p>Over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed, many of which allowing for the missingness to be not at random, in the sense that the unobserved measurements influence the process governing missingness, in addition to influences coming from observed measurements and/or covariates. The fundamental problems that are implied by such models, to which we refer as sensitivity to unverifiable modelling assumptions, has, in turn, sparked off various strands of research in what is now termed sensitivity analysis. The nature of sensitivity originates from the fact that a missingness not at random (MNAR) model is not fully verifiable from the data, rendering the empirical distinction between MNAR and missingness at random (MAR), where only covariates and observed outcomes influence missingness, difficult or even impossible, unless we are willing to accept the posited MNAR model in an unquestioning way. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Of course, such a pair of models will produce different predictions of the unobserved outcomes, given the observed outcomes. Theoretical considerations are supplemented with an illustration that is based on the Slovenian public opinion survey, which has been analysed before in the context of sensitivity analysis.</jats:p>
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spelling Molenberghs, Geert Beunckens, Caroline Sotto, Cristina Kenward, Michael G. 1369-7412 1467-9868 Oxford University Press (OUP) Statistics, Probability and Uncertainty Statistics and Probability http://dx.doi.org/10.1111/j.1467-9868.2007.00640.x <jats:title>Summary</jats:title><jats:p>Over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed, many of which allowing for the missingness to be not at random, in the sense that the unobserved measurements influence the process governing missingness, in addition to influences coming from observed measurements and/or covariates. The fundamental problems that are implied by such models, to which we refer as sensitivity to unverifiable modelling assumptions, has, in turn, sparked off various strands of research in what is now termed sensitivity analysis. The nature of sensitivity originates from the fact that a missingness not at random (MNAR) model is not fully verifiable from the data, rendering the empirical distinction between MNAR and missingness at random (MAR), where only covariates and observed outcomes influence missingness, difficult or even impossible, unless we are willing to accept the posited MNAR model in an unquestioning way. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Of course, such a pair of models will produce different predictions of the unobserved outcomes, given the observed outcomes. Theoretical considerations are supplemented with an illustration that is based on the Slovenian public opinion survey, which has been analysed before in the context of sensitivity analysis.</jats:p> Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit Journal of the Royal Statistical Society Series B: Statistical Methodology
spellingShingle Molenberghs, Geert, Beunckens, Caroline, Sotto, Cristina, Kenward, Michael G., Journal of the Royal Statistical Society Series B: Statistical Methodology, Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit, Statistics, Probability and Uncertainty, Statistics and Probability
title Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_full Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_fullStr Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_full_unstemmed Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_short Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
title_sort every missingness not at random model has a missingness at random counterpart with equal fit
title_unstemmed Every Missingness not at Random Model Has a Missingness at Random Counterpart with Equal Fit
topic Statistics, Probability and Uncertainty, Statistics and Probability
url http://dx.doi.org/10.1111/j.1467-9868.2007.00640.x