Variance Estimation with Imputed Data

1. Variance Estimation with Imputed Data Baltic-Nordic Workshop on Survey Sampling Pauli Ollila

2. Contents of the Session • Survey situation with non-response and imputation • Variances in the presence of non-response • Variance estimation • Examples of variance estimation • No real data examples (ran out of time) Based on the structure of Deliverable 11.1 “Imputation and non-response” of the DACSEIS project concerning variance estimation in different survey situations, available from www.dacseis.de Pauli Ollila

3. Survey Situation with Non-response and Imputation Population and Parameter Pauli Ollila

4. Sampling in Theory and Practice Pauli Ollila

5. Unit and Item Non-response Pauli Ollila

6. Imputation Pauli Ollila

7. Parameter and Its Estimators Pauli Ollila

8. Variance of the Estimator Pauli Ollila

9. Sources of Stochastic Variation of * Pauli Ollila

10. Different Forms of Variance Pauli Ollila

11. Variance Estimation Pauli Ollila

12. Design-based Approach Deterministic Stochastic imputation imputation Pauli Ollila

13. Quasi Design-based Approach with Population Response Mechanism Deterministic imputation Stochastic imputation Pauli Ollila

14. Quasi Design-based Approach - Two-Phase Sampling Deterministic imputation Stochastic imputation Pauli Ollila

15. Model-anticipated Variance Deterministic imputation Stochastic imputation Pauli Ollila

16. Variance Estimation in Multiple Imputation Pauli Ollila

17. Some Remarks on Linearisation and Resampling Methods in the Presence of Non-response and Imputation - The linearisation method usually applies straightforwardly in the estimation of the Vp part of the variance, but the additional terms in the variance can be more problematic. In some cases (e.g. response/non-response “strata” by Cochran or the response as the second phase [with assumptions]) the terms are theoretically clearly justified. For other cases there are some adjustments in order to estimate these terms (see Deliverable 11.1 for more details). Problems arise when the sampling fractions tend not to be small. - The resampling methods should treat the non-response appropriately when creating resamples. This process is not self-evident, especially when there is a without-replacement complex design with stratification of some moderate or large sampling fractions. Specific resampling methods are developed for these situations (see Deliverable 11.1 for more details). Pauli Ollila

18. Example: Jackknife Method for Various Imputation Situations The jackknife method can be transformed to the unit level for variance estimation by using pseudovalues taking the jackknife practice (and the imputation mechanism in it) into account. These terms can utilised within the linearisation approach. Situation without non-response Pseudo-value taking the jackknife “exclusion” (omitting unit j) into account Variance estimator without non-response Weight Weight (j) Estimator Estimator Estimator with exclusion Campbell (1980), Hájek (1981), Rao & Shao (1992), Berger & Rao (2004) Pauli Ollila

19. Mean imputation Stochastic imputation can e.g. be generated from a parametric distribution or it can be the residual of the donor i where Adjusted imputed values and where computed with adjusted imputed values Imputation classes With classification v and Ratio imputation Calculations with Adjusted imputed values See Deliverable 11.1 for further definitions and more details. Pauli Ollila

20. For further information about the methods and list of reference material see DACSEIS-deliverables 11.1 and 11.2 “Imputation and non-response”. Available on the site www.dacseis.de Pauli Ollila