IpfpCov {mipfp}

Covariance matrix of the estimators produced by Ipfp (deprecated)

Description

This function determines the (asymptotic) covariance matrix of the estimates produced by the iterative proportional fitting procedure using the formula designed by Little and Wu (1991).

Usage

IpfpCov(estimate, seed, target.list, replace.zeros = 1e-10)

Arguments

estimate

The array of estimates produced by the Ipfp function.

seed

The intial array (seed) that was updated by the Ipfp function.

target.list

A list of dimensions of the marginal target constrains. Each component of the list is an array whose cells indicate which dimension the corresponding margin relates to.

replace.zeros

If a cell of the estimate or the seed has a value equals to 0, then it is replaced with this value. Default is 1e-10.

Details

The asymptotic covariance matrix of the estimates produced by the iterative proportional fitting procedure has the form (Little and Wu, 1991)

K(K^T D1^{-1} K)^{-1} K^T D2^{-1} K (K^T D1^{-1} K)^{-1} K^T

where

• K is the orthogonal complement of the marginal matrix, i.e. the matrix required to obtain the marginal frequencies;

• D1 is a diagonal matrix of the estimates probabilities;

• D2 is a diagonal matrix of the seed probabilities.

Value

A matrix of dimension length(estimate) x length(estimate) of the asymptotic variance of the proportion estimates produced by Ipfp.

Warning

Note: this function is deprecated, instead use vcov.mipfp.

Author(s)

Johan Barthelemy.

Maintainer: Johan Barthelemy [e-mail].

References

Little, R. J., Wu, M. M. (1991) Models for contingency tables with known margins when target and seed populations differ. Journal of the American Statistical Association 86 (413): 87-95.

See Also

Ipfp function to update an initial multidimensional array with respect to given constraints.

Examples

# true contingency (2-way) table
true.table <- array(c(43, 44, 9, 4), dim = c(2, 2))
# generation of sample, i.e. the seed to be updated
seed <- ceiling(true.table / 10)
# desired targets (margins)
target.row <- apply(true.table, 2, sum)
target.col <- apply(true.table, 1, sum)
# storing the margins in a list
target.data <- list(target.col, target.row)
# list of dimensions of each marginal constrain
target.list <- list(1, 2)
# calling the Ipfp function
res <- Ipfp(seed, target.list, target.data)
# computation of the covariance matrix of the produced estimated probabilities
res.cov <- IpfpCov(res$x.hat, seed, target.list)
# 0.95 level confidence interval of the estimates
n <- sum(res$x.hat)
# ... lower bound
ci.lb <- Array2Vector(res$x.hat) - 1.96 * sqrt(n * diag(res.cov))
# ... upperbound
ci.ub <- Array2Vector(res$x.hat) + 1.96 * sqrt(n * diag(res.cov))