Imputation of Economic Data Subject to Linear Restrictions Using a Sequential Regression Approach

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Imputation of Economic Data Subject to Linear
Restrictions Using a Sequential Regression
Approach

• Caren Tempelman
• Statistics Netherlands
• UNECE 2006, Bonn

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Outline

• Linear restrictions
• Problems with imputing data subject to linear
  restrictions
• Sequential regression
• Conclusions and future research

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Linear restrictions

• Economic data need to satisfy different
• types of linear restrictions, such as
• Balance restrictions
• e.g. Profit turnover - expenses
• Inequality restrictions
• e.g. Non-negativity constraints or the fact that
  
• Nr. of employees Nr. of employees in fte

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Imputation of missing data

• Standard imputation techniques do not take
• linear restrictions on the data into account
• and are therefore highly likely to produce
• imputations that violate these restrictions.
• The need arises for an imputation model
• that can incorporate linear restrictions.

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Imputation model

• We are looking for a model for
  ,
• where and .
• Difficult to find a joint model
• - data consist of several distributional forms
• - how to incorporate restrictions
• Use conditional distributions instead

.
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Sequential regression imputation (1)

• Inspired by MCMC methods
• Use univariate conditional regressions to model
  each variable separately
• Iterate this process so that the final imputed
  values converge to draws from the multivariate
  distribution

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Sequential regression imputation (2)

• The missing items in the variable at
• round t1 are drawn from
• 
  
• which is specified by a regression model.
• Continuous bounded variables
• Truncated regression model
• Semi-continuous bounded variables
• Logistic and truncated regression model

.
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Additional issues

• Advantages
• Extremely flexible, each variable (type) can be
  modelled separately
• Can easily cope with large datasets
• Disadvantages
• Possible incompatibility
• Balance restrictions cannot be straightforwardly
  taken into account

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Incorporating balance restrictions

• If a variable is present in a balance restriction
  
• its value can be derived with certainty from
• the other variables.
• - Eliminate one missing variable from each
• balance restriction
• Choose this variable at random to spread the
  loss
• of quality across variables.

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Conclusions and future research

• Flexible imputation method
• Good preliminary results
• Simulation study to compare this method to other
  methods
• More research into (in)compatibility and
  convergence issues

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• Thank you for your attention!