mice (version 2.14)

pool: Multiple Imputation Pooling

Description

Pools the results of m repeated complete data analysis

Usage

pool(object, method="smallsample")

Arguments

object

An object of class mira, produced by with.mids().

method

A string describing the method to compute the degrees of freedom. The default value is "smallsample", which specifies the is Barnard-Rubin adjusted degrees of freedom (Barnard and Rubin, 1999) for small samples. Specifying a different strin

Value

• An object of class mipo, which stands for 'multiple imputation pooled outcome'. The object is a list containing the following items:
• call
  The call to the pool function.
• call1
  The original call how the mira object was calculated.
• call2
  The original call to the mice function to calculate the underlying midsobject.
• formula
  The formula that is used in call1.
• nmis
  The number of missing entries for each variable.
• m
  The number of imputations
• qhat
  A matrix, containing the estimated coeffients of the m repeated complete data analyses
• u
  The corresponding m variancematrices of the estimates in an three dimensional array.
• qbar
  The pooled estimate, formula (3.1.2) Rubin (1987).
• ubar
  The mean of the variances, formula (3.1.3), Rubin (1987).
• b
  The within imputation variance, formula (3.1.4), Rubin (1987).
• t
  Total variance of the pooled estimates, formula (3.1.5), Rubin (1987).
• r
  Relative increase in variance due to nonresponse, formula (3.1.7), Rubin (1987).
• dfcom
  Degrees of freedom for estimates in the complete data analysis.
• df
  Degrees of freedom for t reference distribution, calculated according to the article of Barnard and Rubin (1999).
• fmi
  Fraction missing information due to nonresponse, formula (3.1.10), Rubin (1987).
• gamma
  Proportion of the total variance explained by the imputations.

Details

The function averages the estimates of the complete data model, computes the total variance over the repeated analyses, and computes the relative increase in variance due to nonresponse and the fraction of missing information. The function relies on the availability of

1. the estimates of the model, typically present as 'coefficients' in the fit object
2. an appropriate estimate of the variance-covariance matrix of the estimates per analyses (estimated byvcov.

The function pools also estimates obtained with lme() and lmer(), BUT only the fixed part of the model.

References

Barnard, J. and Rubin, D.B. (1999). Small sample degrees of freedom with multiple imputation. Biometrika, 86, 948-955. Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons. van Buuren S and Groothuis-Oudshoorn K (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. http://www.jstatsoft.org/v45/i03/

Pinheiro, J.C. and Bates, D.M. (2000). Mixed-Effects Models in S and S-PLUS. Berlin: Springer.

See Also

with.mids, vcov

Examples

# which vcov methods can R find
methods(vcov)

# 
imp <- mice(nhanes)
fit <- with(data=imp,exp=lm(bmi~hyp+chl))
pool(fit)

#Call: pool(object = fit)
#
#Pooled coefficients:
#(Intercept)         hyp         chl 
#  22.01313    -1.45578     0.03459 
#
#Fraction of information about the coefficients missing due to nonresponse: 
#(Intercept)         hyp         chl 
#    0.29571     0.05639     0.38759 
#> summary(pool(fit))
#                 est      se       t     df Pr(>|t|)    lo 95    hi 95 missing
#(Intercept) 22.01313 4.94086  4.4553 12.016 0.000783 11.24954 32.77673      NA
#hyp         -1.45578 2.26789 -0.6419 20.613 0.528006 -6.17752  3.26596       8
#chl          0.03459 0.02829  1.2228  9.347 0.251332 -0.02904  0.09822      10
#               fmi
#(Intercept) 0.29571
#hyp         0.05639
#chl         0.38759
#