Lecture5缺失值处理策略.ppt

The depression trial * * 5. Part II: Multiple imputation * Data set with missing values Result Completed set * * General principles * Informal justification * The algorithm * Pooling information * Hypothesis testing * * MI in practice * MI in practice A simulation-based approach to missing data 1. Generate M 1 plausible versions of . Complete Cases ^ ^ ^ ^ ^ ^ = imputation for Mth dataset 2. Analyze each of the M datasets by standard complete-data methods. 3. Combine the results across the M datasets (M =3-5 is usually OK). * MI in practice... Step 1 Generate M 1 plausible versions of via software, i.e. obtain M different datasets. ? An assumption we make: the data are MCAR or MAR, i.e. the missing data mechanism is ignorable. ? Should use as much information is available in order to achieve the best imputation. ? If the percentage of missing data is high, we need to increase M. * How many datasets to create? The efficiency of an estimator based on M imputations is , where γ is the fraction of missing information. Efficiency of multiple imputation (%) γ M 0.1 0.3 0.5 0.7 0.9 3 97 91 86 81 77 5 98 94 91 88 85 10 99 97 95 93 92 20 100 99 98 97 96 * MI in practice... Step 2 Analyze each of the M datasets by standard complete-data methods. ? Let b be the parameter of interest. ? is the estimate of b from the complete-data analysis of the mth dataset. (m = 1… M) ? is the variance of from the analysis of the mth dataset. * MI in practice... Step 3 Combine the results across the M datasets. ? is the combined inference for b. ? Variance for is between within * Software 1. Joe Schafer’s software from his web site. ($0) /%7Ejls/misoftwa.html Schafer has written publicly available software primarily for S-plus. There is a stand-alone Windows package for data that is multivariate normal. This web site contains much useful information regarding multiple imputatio