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

`pool.compare()`

function.

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 `mira`

(produced by `with.mids()`

or `as.mira()`

), or a `list`

with model fits.

dfcom

A positive number representing the degrees of freedom in the
complete-data analysis. The default (`dfcom = NULL`

) is to
extract this information from the first fitted model. When that fails
the warning `"Large sample assumed"`

is printed, and the
parameter is set `dfcom = 999999`

. Use the `dfcom`

parameter
to specify the correct degrees of freedom.

An object of class `mipo`

, which stands for 'multiple imputation
pooled outcome'.

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 `pool()`

function relies on the `broom::tidy`

and
`broom::glance`

function for extracting this information from a
list of fitted models.

The degrees of freedom calculation uses the Barnard-Rubin adjustment for small samples (Barnard and Rubin, 1999).

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/

```
# NOT RUN {
# 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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