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How Many Imputations Do You Need? A Two-stage Calculation Using a Quadratic Rule

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  • Paul T. von Hippel

Abstract

When using multiple imputation, users often want to know how many imputations they need. An old answer is that 2–10 imputations usually suffice, but this recommendation only addresses the efficiency of point estimates. You may need more imputations if, in addition to efficient point estimates, you also want standard error ( SE ) estimates that would not change (much) if you imputed the data again. For replicable SE estimates, the required number of imputations increases quadratically with the fraction of missing information (not linearly, as previous studies have suggested). I recommend a two-stage procedure in which you conduct a pilot analysis using a small-to-moderate number of imputations, then use the results to calculate the number of imputations that are needed for a final analysis whose SE estimates will have the desired level of replicability. I implement the two-stage procedure using a new SAS macro called %mi_combine and a new Stata command called how_many_imputations.

Suggested Citation

  • Paul T. von Hippel, 2020. "How Many Imputations Do You Need? A Two-stage Calculation Using a Quadratic Rule," Sociological Methods & Research, , vol. 49(3), pages 699-718, August.
    • Handle: RePEc:sae:somere:v:49:y:2020:i:3:p:699-718
    DOI: 10.1177/0049124117747303
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    References listed on IDEAS

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    1. Paul T. von Hippel, 2013. "Should a Normal Imputation Model be Modified to Impute Skewed Variables?," Sociological Methods & Research, , vol. 42(1), pages 105-138, February.
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    1. Franziska Meyer & Oliver Winkler, 2023. "Place of Residence Does Matter for Educational Integration: The Relevance of Spatial Contexts for Refugees’ Transition to VET in Germany," Social Sciences, MDPI, vol. 12(3), pages 1-30, February.
    2. Jieun Lee, 2022. "Moral Hazard on Productivity Among Work-From-Home Workers Amid the COVID-19 Pandemic," Papers 2209.05684, arXiv.org.
    3. Muhammad Salar Khan, 2021. "Estimating a new panel MSK dataset for comparative analyses of national absorptive capacity systems, economic growth, and development in low and middle income economies," Papers 2109.05529, arXiv.org.
    4. Wu Weilun, 2022. "The Impact of Income Inequality on Mortality: A Replication Study of Leigh and Jencks (Journal of Health Economics, 2007)," Economics - The Open-Access, Open-Assessment Journal, De Gruyter, vol. 16(1), pages 229-242, January.
    5. O'Donnell, James & Cárdenas, Diana & Orazani, Nima & Evans, Ann & Reynolds, Katherine J., 2022. "The longitudinal effect of COVID-19 infections and lockdown on mental health and the protective effect of neighbourhood social relations," Social Science & Medicine, Elsevier, vol. 297(C).
    6. Podber, Naomi & Gruenewald, Tara L., 2023. "Positive life experiences and mortality: Examination of psychobiological pathways," Social Science & Medicine, Elsevier, vol. 335(C).
    7. Chaurasia, Ashok, 2023. "Combining rules for F- and Beta-statistics from multiply-imputed data," Econometrics and Statistics, Elsevier, vol. 25(C), pages 51-65.

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