1. 1 G89.2229 Lect 13W Imputation (data augmentation) of missing data Multiple imputation Examples G89.2229 Multiple Regression Week 13 (Wednesday)

2. 2 G89.2229 Lect 13W Missing Data Woes Suppose a subject has completed nearly all of a two hour interview, but forgets (or refuses) to answer a handful of questions. »If these questions are used to define a variable to be included in a model, the subject’s whole record is lost Suppose in a 10 year longitudinal study, a subject misses one annual followup »Listwise deletion results in the full sequence of data being eliminated

3. 3 G89.2229 Lect 13W Model-based ML approaches There are several multivariate methods that can use available data for subjects whose records are incomplete »Structural equation methods »Multilevel methods »Generalized estimating equations »Survival analysis These methods assume that the same model applies to incomplete as well as complete records »Data Missing at Random (MAR)

4. 4 G89.2229 Lect 13W Data Augmentation for Multiple Regression For multiple regression, it is often convenient to use multiple imputation »We generate guesses of what the data might have been had they been observed The guesses use available data and relations among the variables The guesses are constructed to have reasonable variances »We repeat the imputation process 5 or more times

5. 5 G89.2229 Lect 13W Inference from Multiple Imputation Rubin (1987) recommends computing for each regression weight »An average across the K imputations An estimate of the standard error that takes into account the variation over imputations

6. 6 G89.2229 Lect 13W Example

7. 7 G89.2229 Lect 13W Goals of Accounting for Missing Values Adjust for bias »Make use of more representative sample »Don’t let respondents determine the nature of the sample Sometimes increase power »If missing data is limited, including additional cases can help. »Standard errors of individual imputation runs are likely to be smaller

8. 8 G89.2229 Lect 13W Approaches to imputation SPSS has a regression-based approach »Relies on structure of complete cases to infer what the missing cases look like. Newer Bayesian methods iterate to adjust the prediction model for the imputed information. »Uses beliefs or information about distribution form »Example: NORM (free software) http://methodology.psu.edu/mde.html »Example: PROC MI in SAS

9. 9 G89.2229 Lect 13W Some References

10. 10 G89.2229 Lect 13W Some websites Penn State Methodology Center http://methodology.psu.edu/mde.html http://methodology.psu.edu/mde.html Multiple Imputation Online http://www.multiple-imputation.com/ http://www.multiple-imputation.com/ SAS description of PROC MI http://support.sas.com/rnd/app/papers/mi.pdf