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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: Re: Re: st: Situation where multiple imputation may be of no use? |

Date |
Wed, 15 Feb 2012 16:07:36 +0100 |

On Wed, Feb 15, 2012 at 3:40 PM, Stas Kolenikov wrote: > It is unusual that MAR and MCAR led to the same results (although if > you generated the outcome as independent of the covariates except for > treatment, that's how it should be, indeed). This result does not surprise me. Clyde's problem was missing values in the outcome variable, so in both the MAR and MCAR case the probability of missingness is independent of the outcome variable. In that case only using the observed cases in both the MAR and MCAR cases should lead to consistent estimates. Lets say we have an outcome variable y, some treatments and/or covariates x, and a indicator variable m which is 1 when there are missing value an 0 when everything is observed. We want to model y conditional on x, and if we use only the observed cases we get: f(y | x, m== 0) Using Bayes' theorem: f(y | x, m == 0) = f(y, x, m==0) / f(x, m == 0) = { Pr(m==0 | y, x) * f(y | x) * f(x) } / { Pr(m==0 | x) f(x) } In Clyde's case the missing values are in y, and per the MAR assumption the probability of being missing does not depend on y as the MAR assumption states that that probability does not depend on the (unobserved) value of the variable that is missing (otherwise it would be NMAR). As a consequence Pr(m==0 | y, x) = Pr(m==0 | x). So we can write: f(y | x, m== 0 ) = { Pr(m==0 | x) * f(y | x) * f(x) } / { Pr(m==0 | x) f(x) } = f(y | x) Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: Re: Re: st: Situation where multiple imputation may be of no use?***From:*Clyde B Schechter <clyde.schechter@einstein.yu.edu>

**Re: Re: Re: st: Situation where multiple imputation may be of no use?***From:*Stas Kolenikov <skolenik@gmail.com>

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