Single and Multiple Imputation Sample Clauses

Single and Multiple Imputation. In order to retain the sample size of a data set for review in the presence of missing data, a conventional strategy named single imputation is commonly implemented. Specifically, the strategy substitutes each missing value with a reasonable guess or estimate. One simple but popular single-imputation approach is to fill in the missing value with the unconditional mean for the cases that observe the variable. This well-known approach is studied in Haitovsky (1968) and is shown to bias the estimates. Unlike the unconditional mean substitution, regression imputation predicts the most likely value of missing data using a regression model fitted by the observed values of a variable on other variables. Another ad hoc single imputation method is called hot-deck imputation which replaces each missing value with a random draw from the observed values. One comparatively convenient hot-deck approach used in longitudinal studies is last observation carried for- xxxx (LOCF). It sorts the data matrix based on any set of variables and then fills in the missing value with the closest observed value ahead. LOCF is built upon the belief that, for example in a longitudinal study with repeated measurements, the missing measure- ment does not change from the last time it is measured/observed. Little and Xxxxx (2002) and Xxxxxxx (2001) show that single-imputation methods tend to underestimate standard errors since the methods cannot distinguish real data from imputed data and are unable to justify the uncertainty in the imputations. By contrast, multiple imputation (MI) method replaces each missing value with a set of M plausible values. The method is considered as an improvement upon single imputation. Generally, MI procedure consists three steps: 1. imputation step, in which the missing data are imputed and M complete data sets are generated; 2. analysis step, in which a standard statistical technique is applied to analyze each complete data set; 3. combining step, in which the results of the above analyses are combined to provide a final result that accounts for the uncertainty in the data as well as that due to missing values. Figure 1.2 is a pictorial representation of these three steps in a general MI method. We further delve deeply into each step, with introductions of some additional terminologies for MI in the meantime. Incomplete data are considered to have ignorability if they meet the following two con- Figure 1.2: Pictorial representation of three steps in multiple...