# Update an N-way table given target margins This function provides several estimating methods to up multiway table (referred as the seed) subject to known constrains/totals: Iterative proportional fitting procedure (ipfp), maximum likelihood method (ml), minimum chi-squared (chi2) and weighted least squares (lsq). Note that the targets can also be multi-dimensional. ```r Estimate(seed, target.list, target.data, method = "ipfp", keep.input = FALSE, ...) ``` ## Arguments - `seed`: The initial multi-dimensional array to be updated. Each cell must be non-negative if `method` is `ipfp` or strictly positive when `method` is `ml`, `lsq` or `chi2`. - `target.list`: A list of dimensions of the marginal target constrains in `target.data`. Each component of the list is an array whose cells indicate which dimension the corresponding margin relates to. - `target.data`: A list containing the data of the target marginal tables. Each component of the list is an array storing a margin. The list order must follow the ordering defined in `target.list`. Note that the cells of the arrays must be non-negative. - `method`: An optional character string indicating which method is to be used to update the `seed`. This must be on of the strings "ipfp", "ml", "chi2", or "lsq". Default is "ipfp". - `keep.input`: A Boolean indicating if `seed`, `target.data` and `target.list` when set to `TRUE`. - ``...``: Additionals argument that can be passed to the functions Ipfp and ObtainModelEstimates . See their respective documentation for more details. ## Returns An object of class `mipfp` is a list containing at least the following components: - **x.hat**: An array with the same dimension of `seed` whose margins match those specified in `target.list`. - **p.hat**: An array with the same dimension of `x.hat` containing the updated cell probabilities, i.e. `x.hat / sum(x.hat)`. - **error.margins**: A list returning, for each margin, the absolute maximum deviation between the desired and generated margin. - **conv**: A boolean indicating whether the algorithm converged to a solution. - **evol.stp.crit**: The evolution of the stopping criterion over the iterations (if selected `method` is `"ipfp"`)). - **solnp.res**: The estimation process uses the `solnp` optimisation function from the R package Rsolnp and `solnp.res` is the corresponding object returned by the solver (if selected `method` is not `"ipfp"`). - **method**: The selected method for estimation. - **call**: The matched call. The will be also added if `keep.input` has been set to `TRUE`: `seed`, `target.data`, `target.list`. ## References Bacharach, M. (1965). Estimating Nonnegative Matrices from Marginal Data. **International Economic Review** (Blackwell Publishing) 6 (3): 294-310. Bishop, Y. M. M., Fienberg, S. E., Holland, P. W. (1975). **Discrete Multivariate Analysis: Theory and Practice.** MIT Press. ISBN 978-0-262-02113-5. Deming, W. E., Stephan, F. F. (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. Fienberg, S. E. (1970). An Iterative Procedure for Estimation in Contingency Tables. **Annals of Mathematical Statistics** 41 (3): 907-917. Little, R. J., Wu, M. M. (1991) Models for contingency tables with known margins when target and sampled populations differ. **Journal of the American Statistical Association** 86 (413): 87-95. Lang, J.B. (2004) Multinomial-Poisson homogeneous models for contingency tables. **Annals of Statistics** 32(1): 340-383. Stephan, F. F. (1942). Iterative method of adjusting frequency tables when expected margins are known. **Annals of Mathematical Statistics** 13 (2): 166-178. ## Author(s) Johan Barthelemy. Maintainer: Johan Barthelemy johan@uow.edu.au . ## Note It is important to note that if the margins given in `target.list` are not consistent (i.e. the sums of their cells are not equals), the input data is then normalised by considering probabilities instead of frequencies: * the cells of the seed are divided by `sum(seed)`; * the cells of each margin `i` of the list `target.data` are divided by `sum(target.data[[i]])`. ## See Also See the functions `Ipfp` and `ObtainModelEstimates` for more details about the estimation process. `summary.mipfp` for summaries, `vcov.mipfp` for the (asymptotic) covariance of the estimates and `gof.estimates.mipfp` for testing if the seed agrees with the targets. The genereric functions `print` and `coef`. ## Examples ```r # loading the data data(spnamur, package = "mipfp") # subsetting the data frame, keeping only the first 3 variables spnamur.sub <- subset(spnamur, select = Household.type:Prof.status) # true table true.table <- table(spnamur.sub) # extracting the margins tgt.v1 <- apply(true.table, 1, sum) tgt.v1.v2 <- apply(true.table, c(1,2), sum) tgt.v2.v3 <- apply(true.table, c(2,3), sum) tgt.list.dims <- list(1, c(1,2), c(2,3)) tgt.data <- list(tgt.v1, tgt.v1.v2, tgt.v2.v3) # creating the seed, a 10 pct sample of spnamur seed.df <- spnamur.sub[sample(nrow(spnamur), round(0.10*nrow(spnamur))), ] seed.table <- table(seed.df) # applying one fitting method (ipfp) r.ipfp <- Estimate(seed=seed.table, target.list=tgt.list.dims, target.data = tgt.data) print(r.ipfp) ```

Estimate function