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Math Help - Simple question on EM algorithm

  1. #1
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    Simple question on EM algorithm

    Example:

    Let say I have the following data with missing entry:

    time 1 - (79)
    time 2 - (missing)
    time 3 - (79)
    time 4 - (80)
    time 5 - (80)
    time 6 - (78)
    time 7 - (80)


    How can I apply EM-algorithm to treat the missing value?
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  2. #2
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    You need a likelihood to do EM.
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  3. #3
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    Hi,

    I am actually working on 20 missing data and the above is just one of them

    Suppose I run the sas code with code similar to:

    proc mi data=exer seed=12345 simple nimpute=0;
    em itprint outem=outem;
    var y trt time;
    run;

    with the iteration history
    0 1339.684242 81.506276
    1 1326.798995 81.506276
    2 1326.601531 81.539502
    3 1326.597069 81.546350
    4 1326.596953 81.547553
    5 1326.596950 81.547755
    6 1326.596950 81.547789
    7 1326.596950 81.547794
    8 1326.596950 81.547795

    Does it means that I will substitute all missing value with 81.547795 though it's irrelevent in the above context (Since the above missing data should be around 79)?
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  4. #4
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    What exactly are you trying to do? Usually EM is used to estimate MLEs. I'm admittedly not super familiar with EM, but my understanding is that you never actually fill in the missing data per se. You integrate over ALL possible values of the missing data, conditional on current MLE estimates. Given that you need to be taking expectations (it is the Expectation-Maximization algorithm after all) you need to specify the likelihood. EM, at least as far as I know, isn't a way of plugging in the missing values and being on your way as if nothing happened.
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  5. #5
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    In this case the likelihood is unknown which make it hard for me to generate the missing data even when I manage to estimate MLE through the software.. Nevertheless I will try to look into it again.. Thanks again
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