text: Missing Data and Other Opportunities
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  Your next hour:
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  - Measurementerror 
  - Missing data
  - Exercises
  
  Some basic definitions from non-bayesians:
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  - data = observed variable
  - parameter = unobserved variable
  - likelihood = distribution for observed variables
  - prior = distribution for unobserved variables
  
  Waffle-Divorce example (chapter5)
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  Displaying the measurement error of the outcome:
  
  ![](displayingerror.png)
  
  Incorporation of measurementerror on the outcome
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  - = linear regression model 
              +
      replacing the outcome with a vector of parameters
      
  Sounds complicated...let's look again at our waffle-divorce example:
  
     ![](Measurementerror.PNG)
     
  map2stan version of the model:
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  ![](map2stan_me.PNG)
  
  The output:
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  ![](output_me.PNG)
  
  Measurement error on the predictor variable:
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  Nearly the same approach:
  
  ![](me_predictor.PNG)
  
  map2stan version of the model:
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  also just a few changes:
  
  ![](me_pre_map2stan.PNG)
  
  Output:
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  is also nearly the same:
  
  ![](out_pre.PNG)
  
  MISSING DATA
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  Learning how to deal with missing values (MCAR) from the primate milk example (chapter 5):
  
    - In chapter 5 we dropped 12 cases
    - Now: we want do it better by producing estimates for this cases
    - Disadvantage: Wide posteriors
  
  Approach:
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  - N=[0.55,N2,N3,N4,0.65,0.65,.,0.76,0.75]
  - likelihood or prior? - That is the question!
  - both: 
  
    ![](imputing.PNG)
  
  R-code:
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  ![](imp_r.PNG)
  
  What happened with the outcome?
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  ![](modelcomparison.PNG)
  
  Practice example 14M2 (in short form):
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  ![](14M2.PNG)
  
  
  Improving the imputation model:
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  ![](improved_imputation.PNG)
  
  Input & Output:
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  ![](Input_n_output_improved_imp.PNG)
  
  
  