svyreg_huberM function

Huber Robust Survey Regression M- and GM-Estimator

svyreg_huberM and svyreg_huberGM compute, respectively, a survey weighted M- and GM-estimator of regression using the Huber psi-function.

svyreg_huberM(formula, design, k, var = NULL, na.rm = FALSE, asym = FALSE,
              verbose = TRUE, ...)
svyreg_huberGM(formula, design, k, type = c("Mallows", "Schweppe"),
               xwgt, var = NULL, na.rm = FALSE, asym = FALSE, verbose = TRUE,
               ...)

Arguments

• formula: a [formula] object (i.e., symbolic description of the model)
• design: an object of class survey.design; see svydesign.
• k: [double] robustness tuning constant ($0 < k <= Inf$).
• var: a one-sided [formula] object or variable name ([character]) that defines the heteroscedastic variance or [NULL] indicating homoscedastic variance (default: NULL).
• na.rm: [logical] indicating whether NA values should be removed before the computation proceeds (default: FALSE).
• asym: [logical] toggle for asymmetric Huber psi-function (default: FALSE).
• verbose: [logical] indicating whether additional information is printed to the console (default: TRUE).
• type: [character] "Mallows" or "Schweppe".
• xwgt: [numerical vector] or [NULL] of weights in the design space (default: NULL); xwgt is only relevant for type = "Mallows" or type = "Schweppe".
• ...: additional arguments passed to the method (e.g., maxit: maxit number of iterations, etc.).

Details

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

svyreg_huberM and svyreg_huberGM compute, respectively, M- and GM-estimates of regression by iteratively re-weighted least squares (IRWLS). The estimate of regression scale is (by default) computed as the (normalized) weighted median of absolute deviations from the weighted median (MAD; see weighted_mad) for each IRWLS iteration. If the weighted MAD is zero (or nearly so), the scale is computed as the (normalized) weighted interquartile range (IQR).

• M-estimator: The regression M-estimator svyreg_huberM is robust against residual outliers (granted that the tuning constant k is chosen appropriately).

• GM-estimator: Function svyreg_huberGM implements the Mallows and Schweppe regression GM-estimator (see argument type). The regression GM-estimators are robust against residual outliers and outliers in the model's design space (leverage observations; see argument xwgt).

• Numerical optimization: See svyreg_control.

• Models: Models for svyreg_rob are specified symbolically. A typical model has the form response ~ terms, where response

   is the (numeric) response vector and `terms` is a series of terms which specifies a linear predictor for `response`; see `formula` and `lm`.
   
   A formula has an implied intercept term. To remove this use either `y ~ x - 1` or `y ~ 0 + x`; see `formula` for more details of allowed formulae.
  

Failure of convergence

By default, the method assumes a maximum number of maxit = 100

iterations and a numerical tolerance criterion to stop the iterations of tol = 1e-05. If the algorithm fails to converge, you may consider changing the default values; see svyreg_control.

Returns

Object of class svyreg.rob

See Also

Overview (of all implemented functions)

Overview (of all implemented functions)

summary, coef, residuals, fitted, SE and vcov

plot for regression diagnostic plot methods

Other robust estimating methods svyreg_tukeyM and svyreg_tukeyGM

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)
    }

# Compute regression M-estimate with Huber psi-function
m <- svyreg_huberM(payroll ~ employment, dn, k = 8)

# Regression inference
summary(m)

# Extract the coefficients
coef(m)

# Extract variance/ covariance matrix
vcov(m)

# Diagnostic plots (e.g., standardized residuals against fitted values)
plot(m, which = 1L)

# Plot of the robustness weights of the M-estimate against its residuals
plot(residuals(m), robweights(m))