robsurvey (version 0.7)

svymean_ratio: Robust Ratio Predictor of the Mean and Total

Description

Robust ratio predictor (M-estimator) of the population mean and total with Huber and Tukey biweight (bisquare) psi-function.

Usage

svytotal_ratio(object, total, variance = "wu", keep_object = TRUE, ...)
svymean_ratio(object, total, N = NULL, variance = "wu",
              keep_object = TRUE, N_unknown = FALSE, ...)

Value

Object of class svystat_rob

Arguments

object

an object of class [ratio], e.g., result of the Huber ratio \(M\)-estimator svyratio_huber.

total

[numeric] vector of population totals of the auxiliary variables.

N

[numeric] population size (see also N_unknown.

variance

[character] type of variance estimator (default: "wu"); see Details Section.

keep_object

[logical] if TRUE, object is returned as an additional slot of the return value (default: TRUE).

N_unknown

[logical] if TRUE, it is assumed that the population size is unknown; thus, it is estimated (default: FALSE).

...

additional arguments (currently not used).

Details

Package survey must be attached to the search path in order to use the functions (see library or require).

The (robust) ratio predictor of the population total or mean is computed in two steps.

• Step 1: Fit the ratio model associated with the predictor by one of the functions svyratio_huber or svyratio_tukey. The fitted model is called object.

• Step 2: Based on the fitted model obtained in the first step, we predict the population total and mean, respectively, by the predictors svytotal_ratio and svymean_ratio, where object is the fitted ratio model.

Auxiliary data

Two types of auxiliary variables are distinguished: (1) population size \(N\) and (2) the population total of the auxiliary variable (denominator) used in the ratio model.

The option N_unknown = TRUE can be used in the predictor of the population mean if \(N\) is unknown.

Variance estimation

Three variance estimators are implemented (argument variance): "base", "wu", and "hajek". These estimators correspond to the estimators v0, v1, and v2 in Wu (1982).

Utility functions

The return value is an object of class svystat_rob. Thus, the utility functions summary, coef, SE, vcov, residuals, fitted, and robweights are available.

References

Wu, C.-F. (1982). Estimation of Variance of the Ratio Estimator. Biometrika 69, 183--189.

See Also

Overview (of all implemented functions)

svymean_reg and svytotal_reg for (robust) GREG regression predictors

svyreg_huberM, svyreg_huberGM, svyreg_tukeyM and svyreg_tukeyGM for robust regression \(M\)- and \(GM\)-estimators

svymean_huber, svytotal_huber, svymean_tukey and svytotal_tukey for \(M\)-estimators

Examples

head(workplace)

library(survey)
# Survey design for stratified simple random sampling without replacement
dn <- if (packageVersion("survey") >= "4.2") {
        # survey design with pre-calibrated weights
        svydesign(ids = ~ID, strata = ~strat, fpc = ~fpc, weights = ~weight,
                  data = workplace, calibrate.formula = ~-1 + strat)
    } else {
        # legacy mode
        svydesign(ids = ~ID, strata = ~strat, fpc = ~fpc, weights = ~weight,
                  data = workplace)
    }

# Robust ratio M-estimator with Huber psi-function
rat <- svyratio_huber(~payroll, ~ employment, dn, k = 5)

# Summary of the ratio estimate
summary(rat)

# Diagnostic plots of the ration/regression M-estimate (e.g.,
# standardized residuals against fitted values)
plot(rat, which = 1L)

# Plot of the robustness weights of the ratio/regression M-estimate
# against its residuals
plot(residuals(rat), robweights(rat))

# Robust ratio predictor of the population mean
m <- svymean_ratio(rat, total = 1001233, N = 90840)
m

# Summary of the ratio estimate of the population mean
summary(m)

# Extract estimate
coef(m)

# Extract estimate of scale
scale(m)

# Extract estimated standard error
SE(m)