pool function

Pool analysis results obtained from the imputed datasets

pool(
  results,
  conf.level = 0.95,
  alternative = c("two.sided", "less", "greater"),
  type = c("percentile", "normal")
)

## S3 method for class 'pool'
as.data.frame(x, ...)

## S3 method for class 'pool'
print(x, ...)

Arguments

• results: an analysis object created by analyse().
• conf.level: confidence level of the returned confidence interval. Must be a single number between 0 and 1. Default is 0.95.
• alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
• type: a character string of either "percentile" (default) or "normal". Determines what method should be used to calculate the bootstrap confidence intervals. See details. Only used if method_condmean(type = "bootstrap") was specified in the original call to draws().
• x: a pool object generated by pool().
• ...: not used.

Details

The calculation used to generate the point estimate, standard errors and confidence interval depends upon the method specified in the original call to draws(); In particular:

• method_approxbayes() & method_bayes() both use Rubin's rules to pool estimates and variances across multiple imputed datasets, and the Barnard-Rubin rule to pool degree's of freedom; see Little & Rubin (2002).
• method_condmean(type = "bootstrap") uses percentile or normal approximation; see Efron & Tibshirani (1994). Note that for the percentile bootstrap, no standard error is calculated, i.e. the standard errors will be NA in the object / data.frame.
• method_condmean(type = "jackknife") uses the standard jackknife variance formula; see Efron & Tibshirani (1994).
• method_bmlmi uses pooling procedure for Bootstrapped Maximum Likelihood MI (BMLMI). See Von Hippel & Bartlett (2021).

References

Bradley Efron and Robert J Tibshirani. An introduction to the bootstrap. CRC press, 1994. [Section 11]

Roderick J. A. Little and Donald B. Rubin. Statistical Analysis with Missing Data, Second Edition. John Wiley & Sons, Hoboken, New Jersey, 2002. [Section 5.4]

Von Hippel, Paul T and Bartlett, Jonathan W. Maximum likelihood multiple imputation: Faster imputations and consistent standard errors without posterior draws. 2021.