Pool Estimates via Rubin's Rules

Pools point estimates and standard errors from multiple imputations according to Rubin's rules. Degrees of freedom follow the Barnard-Rubin (1999) small-sample adjustment when complete-data degrees of freedom are supplied via edf.

Usage

rubin_pool(est, err, alpha = 0.05, edf = Inf)

Arguments

est

Numeric vector of point estimates, one per imputation.

err

Numeric vector of corresponding standard errors.

alpha

Significance level for the confidence interval. Default 0.05.

edf

Complete-data degrees of freedom (positive scalar or Inf). When finite, the Barnard-Rubin adjusted df are used; default Inf applies the Rubin large-sample df.

Value

A list of class rubin_pool: estimate, std_error, m, var_between, var_within, var_total, df, r, fmi, rel_eff, lcl, ucl, t, p_value (two-sided test against 0), alpha, edf.

Details

With Q_i and U_i the estimate and variance from imputation i, the pooled estimate is the mean of Q_i; total variance T = Ubar + (1 + 1/m) B where Ubar is the mean variance and B the between-imputation variance. The fraction of missing information uses the standard Rubin definition (r + 2/(df+3))/(r+1); the relative efficiency is (1 + lambda/m)^-1. The fraction of missing information and relative efficiency use the final (Barnard-Rubin adjusted) degrees of freedom when edf is finite.

Examples

est = c(0.345, 0.303, 0.298, 0.378)
err = c(0.056, 0.101, 0.099, 0.034)
rubin_pool(est, err)
#> Rubin pooling (m = 4 )
#>   estimate = 0.331000, std_error = 0.088634, df = 58.3
#>   95.0% CI: [0.153597, 0.508403], t = 3.7345, p = 0.0004297, FMI = 0.2521
rubin_pool(est, err, edf = 120)
#> Rubin pooling (m = 4 )
#>   estimate = 0.331000, std_error = 0.088634, df = 35.6
#>   95.0% CI: [0.151165, 0.510835], t = 3.7345, p = 0.0006572, FMI = 0.2670