Regression imputation with linear constraints on the variables

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Regression imputation with linear constraints on
the variables
Jeroen Pannekoek Statistics Netherlands

• Work Session on Statistical Data Editing
• (Bonn, Germany, 25-27 September 2006)

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Overview

• Definition of the problem
• Consistent linear regression predictions
• Other models

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Balance edits

• Example of balance edits 5 variables, 2
  constraints

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Constraints on missing values

• Suppose that some part of y is missing
• Partitioning of y and R gives

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Regression predictions and adjustments

• Standard regression imputation

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A model incorporating the predictions
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Parameter estimates

• Estimates for ai and ß in the simultaneous
  model

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Illustration
Constraints not a nuisance but a benefit !
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Weighted adjustments

• Suppose that

and we want to make larger adjustments for
variables with larger error variance
minimize
subject to
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WLS normal equations

• Minimize

w.r.t ß and ai yields normaL equations
The last equation shows consistency of the
predictions
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Log transform

• Model