Pool multiply imputed estimates by Rubin's rules

Rubin (1987) pooling with the Barnard and Rubin (1999) degrees of freedom, as mice::pool.scalar: the fraction of missing information is \((r + 2/(\nu + 3)) / (r + 1)\) and the relative efficiency \(1 / (1 + \gamma / m)\).

Usage

rubins_rules(estimates, variances, confidence = 0.95, dfcom = Inf)

Arguments

estimates: Numeric vector of the m point estimates.
variances: Numeric vector of the m within-imputation variances.
confidence: Confidence level of the interval. Default 0.95.
dfcom: Complete-data degrees of freedom for the small-sample adjustment; Inf gives Rubin's large-sample df.

Value

A list with estimate, within_variance, between_variance, total_variance, standard_error, df, ci_lower, ci_upper, fmi, relative_efficiency, lambda_hat and method.

References

Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley. Barnard, J. and Rubin, D. B. (1999). Small-sample degrees of freedom with multiple imputation. Biometrika 86, 948-955.

Examples

rubins_rules(c(1.2, 1.5, 1.1, 1.4, 1.3), c(0.04, 0.05, 0.045, 0.05, 0.042))
#> $estimate
#> [1] 1.3
#> 
#> $within_variance
#> [1] 0.0454
#> 
#> $between_variance
#> [1] 0.025
#> 
#> $total_variance
#> [1] 0.0754
#> 
#> $standard_error
#> [1] 0.2745906
#> 
#> $df
#> [1] 25.26738
#> 
#> $ci_lower
#> [1] 0.7347734
#> 
#> $ci_upper
#> [1] 1.865227
#> 
#> $fmi
#> [1] 0.4404799
#> 
#> $relative_efficiency
#> [1] 0.9190366
#> 
#> $lambda_hat
#> [1] 0.397878
#> 
#> $method
#> [1] "Rubin's rules"
#>