Combine estimates by Rubin's rules
The pool() function combines the estimates from m
repeated complete data analyses. The typical sequence of steps to
do a multiple imputation analysis is:
Impute the missing data by the mice function, resulting in
a multiple imputed data set (class mids);
Fit the model of interest (scientific model) on each imputed data set
by the with() function, resulting an object of class mira;
Pool the estimates from each model into a single set of estimates
and standard errors, resulting is an object of class mipo;
Optionally, compare pooled estimates from different scientific models
by the D1() or D3() functions.
A common error is to reverse steps 2 and 3, i.e., to pool the
multiply-imputed data instead of the estimates. Doing so may severely bias
the estimates of scientific interest and yield incorrect statistical
intervals and p-values. The pool() function will detect
this case.
pool(object, dfcom = NULL)
object |
An object of class |
dfcom |
A positive number representing the degrees of freedom in the
complete-data analysis. Normally, this would be the number of independent
observation minus the number of fitted parameters. The default
( |
The pool() function averages the estimates of the complete
data model, computes the
total variance over the repeated analyses by Rubin's rules
(Rubin, 1987, p. 76),
and computes the following diagnostic statistics per estimate:
Relative increase in variance due to nonresponse r;
Residual degrees of freedom for hypothesis testing df;
Proportion of total variance due to missingness lambda;
Fraction of missing information fmi.
The function requires the following input from each fitted model:
the estimates of the model, usually obtainable by coef()
the standard error of each estimate;
the residual degrees of freedom of the model.
The degrees of freedom calculation for the pooled estimates uses the Barnard-Rubin adjustment for small samples (Barnard and Rubin, 1999).
The pool() function relies on the broom::tidy for
extracting the parameters. Versions before mice 3.8.5 failed
when no broom::glance() function was found for extracting the
residual degrees of freedom. The pool() function is now
more forgiving.
In versions prior to mice 3.0 pooling required only that
coef() and vcov() methods were available for fitted
objects. This feature is no longer supported. The reason is that vcov()
methods are inconsistent across packages, leading to buggy behaviour
of the pool() function.
Since mice 3.0+, the broom
package takes care of filtering out the relevant parts of the
complete-data analysis. It may happen that you'll see the messages
like Error: No tidy method for objects of class ... or
Error: No glance method for objects of class .... The message
means that your complete-data method used in with(imp, ...) has
no tidy or glance method defined in the broom package.
The broom.mixed package contains tidy and glance methods
for mixed models. If you are using a mixed model, first run
library(broom.mixed) before calling pool().
If no tidy or glance methods are defined for your analysis
tabulate the m parameter estimates and their variance
estimates (the square of the standard errors) from the m fitted
models stored in fit$analyses. For each parameter, run
pool.scalar to obtain the pooled parameters estimate, its variance, the
degrees of freedom, the relative increase in variance and the fraction of missing
information.
An alternative is to write your own glance() and tidy()
methods and add these to broom according to the specifications
given in https://broom.tidymodels.org.
An object of class mipo, which stands for 'multiple imputation
pooled outcome'.
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. https://www.jstatsoft.org/v45/i03/
# pool using the classic MICE workflow imp <- mice(nhanes, maxit = 2, m = 2) fit <- with(data = imp, exp = lm(bmi ~ hyp + chl)) summary(pool(fit))
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