1 / 11

Regression imputation with linear constraints on the variables

Regression imputation with linear constraints on the variables. Jeroen Pannekoek Statistics Netherlands. Work Session on Statistical Data Editing (Bonn, Germany, 25-27 September 2006). Overview. Definition of the problem Consistent linear regression predictions Other models.

orien
Download Presentation

Regression imputation with linear constraints on the variables

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Regression imputation with linear constraints on the variables Jeroen Pannekoek Statistics Netherlands Work Session on Statistical Data Editing (Bonn, Germany, 25-27 September 2006)

  2. Overview • Definition of the problem • Consistent linear regression predictions • Other models

  3. Balance edits • Example of balance edits: 5 variables, 2 constraints

  4. We need predictions that satisfy Constraints on missing values • Suppose that some part of y is missing • Partitioning of y and R gives:

  5. Taking care of constraints is a minimum size adjustment obtained by: Minimize subject to => and so where Regression predictions and adjustments • Standard regression imputation

  6. Consider the model and estimate the parameters simultaneously by OLS. This leads to normal equations: (1) (2) To be solved for α and β (2) Shows that the predictions are consistent A model incorporating the predictions

  7. For records with missing values use: Parameter estimates • Estimates for αi and β in the simultaneous model:

  8. Illustration Constraints: not a nuisance but a benefit !

  9. This leads to predictions of the form: And this model can be estimated bij WLS Weighted adjustments • Suppose that and we want to make larger adjustments for variables with larger error variance: minimize subject to

  10. WLS normal equations • Minimize w.r.t β and αi yields normaL equations The last equation shows consistency of the predictions

  11. Estimate by WLS using covariance matrix Results in normal equations The last equation shows again consistency of the predictions Log transform • Model

More Related