Full Information Maximum Likelihood (FIML) Estimation

Full information maximum likelihood estimates a regression from every observed value by maximising the multivariate normal likelihood of each case's observed variables, without deleting incomplete cases.

불완전한 사례를 지우지 않고, 사례마다 관측된 변수의 다변량 정규 우도를 최대화해 모든 관측값으로 회귀를 추정하는 방법입니다.

Several predictors in my regression have missing values and listwise deletion drops a third of the sample. Can I estimate the model using all available data?

회귀의 설명변수 몇 개에 결측이 있어서 목록별 삭제를 하면 표본의 3분의 1이 사라져요. 있는 자료를 모두 써서 추정할 수 있나요?

Use full information maximum likelihood: the means and covariances of the outcome, predictors and optional auxiliary variables are estimated by maximum likelihood with the EM algorithm using every observed value, and the regression coefficients follow from those moments. Under missing at random and multivariate normality the estimates are consistent, and standard errors come from the observed information matrix.

When to use Full Information Maximum Likelihood (FIML) Estimation

• Outcome and predictors both have missing values under a plausible MAR mechanism.
• You want a single-run alternative to multiple imputation for a linear regression.
• You have auxiliary variables that predict missingness but are not part of the model.

When to use something else

• Variables are strongly non-normal or categorical; use multiple imputation with suitable models instead.
• Missingness depends on the unobserved values themselves; run a tipping-point or selection-model sensitivity analysis instead.

Assumptions and requirements

• Data are missing at random given the variables in the model and the auxiliaries.
• Variables are jointly multivariate normal (no robust correction is applied).
• At most 20 variables in total.

What the analysis reports

• Intercept, slopes and residual variance with observed-information standard errors, z, p and CI
• Listwise-deletion estimates for comparison
• Log-likelihood, R² and EM iterations
• Number of complete cases and percentage of missing cells

How to report it

Using full information maximum likelihood (n = [value], [value]% missing cells), [predictor] predicted [outcome], b = [value], SE = [value], z = [value], p = [value], 95% CI [[value], [value]]; R² = [value].

Related methods

• Multiple Imputation (MICE) with Pooled Regression
• Little's MCAR Test
• Structural Equation Modeling

Run Full Information Maximum Likelihood (FIML) Estimation on Quorant