WIPF: Weighted Iterative Proportional Fitting (WIPF) in N (greater...

In WIPF: Weighted Iterative Proportional Fitting

Weighted Iterative Proportional Fitting (WIPF) in N (greater than 1) dimensions

Description

Implements the Weighted Iterative Proportional Fitting (WIPF) algorithm to adjust an N-dimensional array subject to weighted marginal constraints.

Usage

WIPF(
  seed,
  weights,
  margins,
  indices,
  normalize = TRUE,
  tol = 10^-6,
  maxit = 1000,
  full = FALSE,
  ...
)

Arguments

seed	An N-dimensional array of non-negative values with the initial values.
weights	An N-dimensional array of non-negative values with the weights associated to each entry of the seed array.
margins	A list of arrays of non-negative values of order less than N with the target (weighted) marginal sums over the specified dimensions.
indices	A list of vectors with the same length as margins, indicating the indices corresponding to each array in margins.
normalize	TRUE/FALSE argument indicating whether the weights should be normalized across all dimensions before constructing the weighted sums for comparison with the margin values. Default is TRUE. Normalization is essential when adjusting a set of indices for which the margins represent theoretical convex combinations of the inner indices. This characterizes a typical context in which WIPF may be of value.
tol	Stopping criterion. The algorithm stops when the maximum difference between the weighted sums of the values to be fitted and the margins is lower than the value specified by tol. Default, 0.000001.
maxit	Stopping criterion. A positive integer number indicating the maximum number of iterations allowed. Default, 1000. The algorithm will stop if the values to be fitted still has not converged after these many iterations.
full	TRUE/FALSE argument indicating if either only the solution should be saved or a more complete output. Default FALSE.
...	Other arguments to be passed to the function. Not currently used.

Details

The function updates an initial N-dimensional array (referred to as the seed) using an N-dimensional array of weights to align with a collection of lower-dimensional margins of different orders, some of which may be missing. When all provided margins are compatible given the weights, the updated array ensures that the corresponding weighted sums over all specified index subsets coincide with the supplied margins. If the provided margins are incompatible given the weights, the functions WIPF1 and WIPF are applied to the provided margins to guarantee their compatibility with the weights. In these cases, the margins are updated in increasing order of sub-indices, with higher-order indices running faster.

Value

When full = FALSE an object similar to seed with the solution reached when the algorithm stops. When full = TRUE a list with the following components:

sol	An object similar to seed with the solution reached at convergence (or when the maximum number of iterations is reached).
iter	Number of iterations when the algorithm stops.
margins	A list of arrays similar margins with the actual margins used to reach the solution. Each array whose margins are compatible given the weights coincides with the original array.
dev.margins	A list of arrays similar to the margins output containing the absolute maximum deviations between the values in margins and the corresponding weighted sums of the values in sol.
dev.congruence	A list of arrays, similar to the margins output, containing the differences between the values in margins and those in inputs$margins. In other words, it shows the difference between the final margins actually used (after adjusting them, if necessary, to be compatible with the weights) and the original margins provided by the user.
inputs	A list containing all the objects with the values used as arguments by the function.

Note

Weighted Iterative Proportional Fitting is an extension of IPF. WIPF produces the same solutions than IPF with all weights being ones and when they are not normalized. IPF is also known as RAS in economics, raking in survey research or matrix scaling in computer science.

Author(s)

Jose M. Pavia, [e-mail]

Examples

s <- structure(c(0.9297, 0.9446, 0.8763, 0.92, 0.8655, 0.8583, 0.8132,
                 0.8679, 0.7968, 0.7834, 0.721, 0.7859, 0.7747, 0.7851, 0.8632,
                 1.041, 1.5617, 1.5642, 1.4847, 1.5176, 1.4157, 1.3851, 1.3456,
                 1.4012, 1.3017, 1.2626, 1.1904, 1.2668, 1.3203, 1.3181, 1.1965,
                 1.1654, 1.2219, 1.3863, 1.306, 1.1963, 1.1376, 1.35, 1.2595,
                 1.1289, 1.0456, 1.2863, 1.1274, 1.0208, 1.0542, 1.1272, 1.1594,
                 1.1668, 1.1931, 1.1328, 1.1221, 1.1011, 1.1298, 1.0454, 1.0573,
                 1.0557, 1.0599, 0.973, 0.9545, 0.9721, 1.0489, 0.9934, 0.9382,
                 0.876, 1.339, 1.1939, 1.0229, 1.0378, 1.0402, 0.9554, 0.9794,
                 1.0089, 0.9422, 0.8584, 0.8563, 0.9013, 0.9252, 0.8706, 0.8354,
                 0.8071, 0.9737, 1.0008, 0.9593, 0.9257, 0.9556, 0.9534, 0.9313,
                 0.9151, 0.883, 0.8731, 0.8285, 0.8309, 0.9131, 0.9258, 0.8467,
                 0.7785), .Dim = c(4L, 4L, 6L))
w <- structure(c(18520.3, 11776.3, 19479.5, 22497.6, 18968.7, 17263.7,
                 36494.7, 21707, 13406.3, 13570.4, 37746.1, 20593.2, 6595.6, 25444.6,
                 59868.2, 81777.2, 3380.4, 20610.7, 22247.3, 6800.9, 5236.3, 14877.8,
                 7205, 5028.4, 1130.7, 6603.2, 4007.4, 2620.5, 374.8, 1624.3,
                 4963.7, 9551.3, 31806, 93615.9, 121986.6, 44640.3, 32110.6, 95814.4,
                 72827.9, 30922.5, 43197.3, 72050.8, 66673.4, 40370.1, 31488.2,
                 55014.9, 69457.2, 80021.2, 17701.7, 8765.2, 11790.9, 3872.8,
                 30544.5, 12141.2, 12415.2, 9471.9, 36138.6, 19198.1, 23120.1,
                 15597.9, 12140.2, 8058.3, 20948.3, 19380.2, 78543.9, 86503.6,
                 28727.8, 29208.7, 26300.6, 42363, 20786.6, 14380.3, 9493.5, 17816.2,
                 19844.1, 10898.2, 1419, 4211.5, 20615, 22748.2, 3365.8, 2639.8,
                 2433.3, 930.5, 22119.6, 31022.7, 12748.5, 10161.4, 15450.2, 32747.1,
                 22596.4, 13228.1, 17289.2, 30189.2, 31476.6, 15338.7),
                .Dim = c(4L, 4L, 6L))
m1 <- c(1.025527, 1.018229, 0.969744, 0.994998)
m2 <- c(1.111023, 1.030213, 0.935041, 0.906709)
m3 <- c(0.810568, 1.375203, 1.07096, 1.044461, 0.949441, 0.915284)
m12 <- structure(c(1.061059, 1.120345, 1.097519, 1.188501, 1.017091,
                   0.967245, 1.03447, 1.18867, 0.9797, 0.900885, 0.85575, 1.070772,
                   1.041953, 1.074653, 0.887316, 0.791906), .Dim = c(4L, 4L))
m13 <- structure(c(0.779029, 0.865343, 0.757887, 0.852708, 1.351367,
                   1.409585, 1.350907, 1.361528, 1.091867, 1.107661, 0.99364, 1.127478,
                   1.13439, 0.948428, 1.075919, 0.916096, 1.031958, 0.835103, 1.006321,
                   0.982888, 0.86109, 0.976673, 0.961731, 0.764211), .Dim = c(4L, 6L))
m23 <- structure(c(0.962955, 0.880973, 0.798545, 0.714783, 1.547556,
                   1.277098, 1.149491, 1.210108, 1.186342, 1.084436, 0.976822, 1.003611,
                   1.092564, 1.066306, 1.038601, 0.996779, 0.971751, 1.016173, 0.867197,
                   0.803929, 0.831913, 0.933863, 0.857392, 0.960169), .Dim = c(4L, 6L))

m <- list(m1, m3, m12, m23)
ind <- list(1, 3, c(1, 2), c(2, 3))


example <- WIPF(seed = s, weights = w, margins = m, indices = ind)

WIPF documentation built on March 7, 2026, 1:07 a.m.