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Pool analysis results obtained from the imputed datasets

Source: R/pool.R
pool.Rd

Pool analysis results obtained from the imputed datasets

Usage 

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, ...)

mcse(x, results)

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

# S3 method for class 'mcse'
print(x, ..., pval_digits = 2, pval_eps = 1e-06, pval_nsmall = 5)

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.

pval_digits

number of significant digits to print for p-values' MCSE.

pval_eps

the minimum p-values' MCSE to print.

pval_nsmall

the minimum number of digits to print for p-values' MCSE.

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). Here, the mcse() function can compute the Monte Carlo standard error (MCSE) of the pooled estimates, via a Jackknife variance estimator for all parameters; see Efron & Gong (1983) and Royston, Carlin & White (2009).

  • 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]

Bradley Efron and Gail Gong. A leisurely look at the bootstrap, the jackknife, and cross-validation. The American Statistician, 37(1):36-48, 1983.

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]

Royston, P., Carlin, J. B., & White, I. R. Multiple imputation of missing values: New features for mim. Stata Journal, 9(2): 252-264, 2009.

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