Multiple Imputation (MICE) with Pooled Regression

Multiple imputation by chained equations (MICE) fills each missing value several times from conditional models, fits the analysis model to every completed dataset, and pools the results with Rubin's rules.

연쇄방정식 다중대체(MICE)는 결측값을 조건부 모형으로 여러 번 대체하고, 각 대체 자료에 분석 모형을 적합한 뒤 Rubin 규칙으로 결과를 합치는 방법이다.

My regression predictors have missing values; how do I impute them properly and still get correct standard errors?

회귀분석 설명변수에 결측이 있는데, 표준오차까지 제대로 나오게 대체하려면 어떻게 하나요?

MICE creates m completed datasets by cycling through regression-based imputation models for each incomplete variable, then fits the same regression to each dataset. Rubin's rules average the coefficients and add the between-imputation variance to the within-imputation variance, so the standard errors reflect uncertainty due to missingness.

When to use Multiple Imputation (MICE) with Pooled Regression

• Predictors or the outcome have missing values that are plausibly missing at random
• Complete-case analysis would discard a substantial share of cases
• You need valid standard errors and confidence intervals after imputation

When to use something else

• Missingness depends on the unobserved values themselves; use selection or pattern-mixture sensitivity models instead
• Only a handful of values are missing completely at random; complete-case analysis is simpler and unbiased

Assumptions and requirements

• Data are missing at random given the variables in the imputation model
• Imputation models are compatible with the analysis model
• Enough imputations for the fraction of missing information
• The analysis model is an ordinary least squares regression of the outcome on the predictors

What the analysis reports

• Pooled coefficients and standard errors
• Barnard–Rubin degrees of freedom and p values
• Fraction of missing information per coefficient
• Complete-case estimates for comparison

How to report it

Missing data were handled by multiple imputation (m = [value]); the pooled coefficient for [predictor] was b = [value], SE = [value], 95% CI [[value], [value]], fraction of missing information = [value].

Related methods

• Little's MCAR Test
• Missing Data Pattern Analysis
• Multiple Linear Regression

Run Multiple Imputation (MICE) with Pooled Regression on Quorant