# ipu2: Iterative Proportional Updating In statistikat/simPop: Simulation of Synthetic Populations for Survey Data Considering Auxiliary Information

## Description

Adjust sampling weights to given totals based on household-level and/or individual level constraints.

## Usage

 1 2 3 4 5 ipu2(dat, hid = NULL, conP = NULL, conH = NULL, epsP = 1e-06, epsH = 0.01, verbose = FALSE, w = NULL, bound = 4, maxIter = 200, meanHH = TRUE, allPthenH = TRUE, returnNA = TRUE, looseH = FALSE, numericalWeighting = computeLinear, check_hh_vars = TRUE, conversion_messages = FALSE) 

## Arguments

 dat a data.table containing household ids (optionally), base weights (optionally), household and/or personal level variables (numerical or categorical) that should be fitted. hid name of the column containing the household-ids within dat or NULL if such a variable does not exist. conP list or (partly) named list defining the constraints on person level. The list elements are contingency tables in array representation with dimnames corresponding to the names of the relevant calibration variables in dat. If a numerical variable is to be calibrated, the respective list element has to be named with the name of that numerical variable. Otherwise the list element shoud NOT be named. conH list or (partly) named list defining the constraints on household level. The list elements are contingency tables in array representation with dimnames corresponding to the names of the relevant calibration variables in dat. If a numerical variable is to be calibrated, the respective list element has to be named with the name of that numerical variable. Otherwise the list element shoud NOT be named. epsP numeric value or list (of numeric values and/or arrays) specifying the convergence limit(s) for conP. The list can contain numeric values and/or arrays which must appear in the same order as the corresponding constraints in conP. Also, an array must have the same dimensions and dimnames as the corresponding constraint in conP. epsH numeric value or list (of numeric values and/or arrays) specifying the convergence limit(s) for conH. The list can contain numeric values and/or arrays which must appear in the same order as the corresponding constraints in conH. Also, an array must have the same dimensions and dimnames as the corresponding constraint in conH. verbose if TRUE, some progress information will be printed. w name if the column containing the base weights within dat or NULL if such a variable does not exist. In the latter case, every observation in dat is assigned a starting weight of 1. bound numeric value specifying the multiplier for determining the weight trimming boundary if the change of the base weights should be restricted, i.e. if the weights should stay between 1/bound*w and bound*w. maxIter numeric value specifying the maximum number of iterations that should be performed. meanHH if TRUE, every person in a household is assigned the mean of the person weights corresponding to the household. If "geometric", the geometric mean is used rather than the arithmetic mean. allPthenH if TRUE, all the person level calibration steps are performed before the houshold level calibration steps (and meanHH, if specified). If FALSE, the houshold level calibration steps (and meanHH, if specified) are performed after everey person level calibration step. This can lead to better convergence properties in certain cases but also means that the total number of calibration steps is increased. returnNA if TRUE, the calibrated weight will be set to NA in case of no convergence. looseH if FALSE, the actual constraints conH are used for calibrating all the hh weights. If TRUE, only the weights for which the lower and upper thresholds defined by conH and epsH are exceeded are calibrated. They are however not calibrated against the actual constraints conH but against these lower and upper thresholds, i.e. conH-conH*epsH and conH+conH*epsH. numericalWeighting See numericalWeighting check_hh_vars If TRUE check for non-unique values inside of a household for variables in household constraints conversion_messages show a message, if inputs need to be reformatted. This can be useful for speed optimizations if ipu2 is called several times with similar inputs (for example bootstrapping)

## Details

This function implements the weighting procedure described here.

conP and conH are contingency tables, which can be created with xtabs. The dimnames of those tables should match the names and levels of the corresponding columns in dat.

maxIter, epsP and epsH are the stopping criteria. epsP and epsH describe relative tolerances in the sense that \deqn{1-epsP < \frac{w_{i+1}}{w_i} < 1+epsP}{1-epsP < w(i+1)/w(i) < 1+epsP} will be used as convergence criterium. Here i is the iteration step and wi is the weight of a specific person at step i.

The algorithm performs best if all varables occuring in the constraints (conP and conH) as well as the household variable are coded as factor-columns in dat. Otherwise, conversions will be necessary which can be monitored with the conversion_messages argument. Setting check_hh_vars to FALSE can also incease the performance of the scheme.

## Value

The function will return the input data dat with the calibrated weights calibWeight as an additional column as well as attributes. If no convergence has been reached in maxIter steps, and returnNA is TRUE (the default), the column calibWeights will only consist of NAs. The attributes of the table are attributes derived from the data.table class as well as the following.

 converged Did the algorithm converge in maxIter steps? iterations The number of iterations performed. conP, conH, epsP, epsH See Arguments. conP_adj, conH_adj Adjusted versions of conP and conH formP, formH Formulas that were used to calculate conP_adj and conH_adj based on the output table.

## Author(s)

Alexander Kowarik, Gregor de Cillia

ipu
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 data(eusilcS) setDT(eusilcS) eusilcS <- eusilcS[, list(db030,hsize,db040,age,rb090,netIncome,db090,rb050)] ## rename columns setnames(eusilcS, "rb090", "gender") setnames(eusilcS, "db040", "state") setnames(eusilcS, "db030", "household") setnames(eusilcS, "rb050", "weight") ## some recoding # generate age groups eusilcS[, agegroup := cut(age, c(-Inf, 10*1:9, Inf), right = FALSE)] # some recoding of netIncome for reasons of simplicity eusilcS[is.na(netIncome), netIncome := 0] eusilcS[netIncome < 0, netIncome := 0] # set hsize to 1,...,5+ eusilcS[, hsize := cut(hsize, c(0:4, Inf), labels = c(1:4, "5+"))] # treat households as a factor variable eusilcS[, household := as.factor(household)] ## example for base weights assuming a simple random sample of households stratified per region eusilcS[, regSamp := .N, by = state] eusilcS[, regPop := sum(weight), by = state] eusilcS[, baseWeight := regPop/regSamp] ## constraints on person level # age conP1 <- xtabs(weight ~ agegroup, data = eusilcS) # gender by region conP2 <- xtabs(weight ~ gender + state, data = eusilcS) # personal net income by gender conP3 <- xtabs(weight*netIncome ~ gender, data = eusilcS) ## constraints on household level conH1 <- xtabs(weight ~ hsize + state, data = eusilcS, subset = !duplicated(household)) # array of convergence limits for conH1 epsH1 <- conH1 epsH1[1:4,] <- 0.005 epsH1["5+",] <- 0.2 # without array epsH1 calibweights1 <- ipu2(eusilcS, hid = "household", conP = list(conP1, conP2, netIncome = conP3), conH = list(conH1), epsP = list(1e-06, 1e-06, 1e-03), epsH = 0.01, bound = NULL, verbose = TRUE, maxIter = 200) # with array epsH1, base weights and bound calibweights2 <- ipu2(eusilcS, hid = "household", conP = list(conP1, conP2), conH = list(conH1), epsP = 1e-06, epsH = list(epsH1), w = "baseWeight", bound = 4, verbose = TRUE, maxIter = 200) # show an adjusted version of conP and the original attr(calibweights2, "conP_adj") attr(calibweights2, "conP")