Adjustment of marginal distributions using iterative proportional fitting

Adjusts the marginal distributions for group and unit in source to the respective marginal distributions in target, using the iterative proportional fitting algorithm (IPF).

Usage

ipf(
  source,
  target,
  group,
  unit,
  weight = NULL,
  max_iterations = 100,
  precision = 1e-04
)

Arguments

source

A "source" data frame. The marginals of this dataset are adjusted to the marginals of target.

target

A "target" data frame. The function returns a dataset where the marginal distributions of group and unit categories are approximated by those of target.

group

A categorical variable or a vector of variables contained in source and target. Defines the first distribution for adjustment.

unit

A categorical variable or a vector of variables contained in source and target. Defines the second distribution for adjustment.

weight

Numeric. (Default NULL)

max_iterations

Maximum number of iterations used for the IPF algorithm.

precision

Convergence criterion for the IPF algorithm. In every iteration, the ratio of the source and target marginals are calculated for every category of group and unit. The algorithm converges when all ratios are smaller than 1 + precision.

Value

Returns a data frame that retains the association structure of source while approximating the marginal distributions for group and unit of target. The dataset identifies each combination of group and unit, and categories that only occur in either source or target are dropped. The adjusted frequency of each combination is given by the column n, while n_target and n_source contain the zero-adjusted frequencies in the target and source dataset, respectively.

Details

The algorithm works by scaling the marginal distribution of group in the source data frame towards the marginal distribution of target; then repeating this process for unit. The algorithm then keeps alternating between group and unit until the marginals of the adjusted data frame are within the allowed precision. This results in a dataset that retains the association structure of source while approximating the marginal distribution of target. If the number of unit and group categories is different in source and target, the data frame returns the combination of unit and group categories that occur in both datasets. Zero values are replaced by a small, non-zero number (1e-4). Note that the values returned sum to the observations of the source data frame, not the target data frame. This is different from other IPF implementations, but ensures that the IPF does not change the number of observations.

References

W. E. Deming and F. F. Stephan. 1940. "On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known". Annals of Mathematical Statistics. 11 (4): 427–444.

T. Karmel and M. Maclachlan. 1988. "Occupational Sex Segregation — Increasing or Decreasing?" Economic Record 64: 187-195.

Examples

if (FALSE) {
# adjusts the marginals of group and unit categories so that
# schools00 has similar marginals as schools05
adj <- ipf(schools00, schools05, "race", "school", weight = "n")

# check that the new "race" marginals are similar to the target marginals
# (the same could be done for schools)
aggregate(adj$n, list(adj$race), sum)
aggregate(adj$n_target, list(adj$race), sum)

# note that the adjusted dataset contains fewer
# schools than either the source or the target dataset,
# because the marginals are only defined for the overlap
# of schools
length(unique(schools00$school))
length(unique(schools05$school))
length(unique(adj$school))
}