Fractional Weighted Bootstrap Covariance Matrix Estimation

vcovFWB() estimates the covariance matrix of model coefficient estimates using the fractional weighted bootstrap. It serves as a drop-in for stats::vcov() or sandwich::vcovBS(). Clustered covariances are can be requested.

Usage

vcovFWB(
  x,
  cluster = NULL,
  R = 1000,
  start = FALSE,
  wtype = getOption("fwb_wtype", "exp"),
  ...,
  fix = FALSE,
  use = "pairwise.complete.obs",
  .coef = stats::coef,
  verbose = FALSE,
  cl = NULL
)

Arguments

x: a fitted model object, such as the output of a call to lm() or glm(). The model object must result from a function that can be updated using update() and has a weights argument to input non-integer case weights.
cluster: a variable indicating the clustering of observations, a list (or data.frame) thereof, or a formula specifying which variables from the fitted model should be used (see examples). By default (cluster = NULL), either attr(x, "cluster") is used (if any) or otherwise every observation is assumed to be its own cluster.
R: the number of bootstrap replications.
start: logical; should .coef(x) be passed as start to the update(x, weights = ...) call? In case the model x is computed by some numeric iteration, this may speed up the bootstrapping.
wtype: string; the type of weights to use. Allowable options include "exp" (the default), "pois", "multinom", and "mammen". See fwb() for details. See set_fwb_wtype() to set a global default.
...: ignored.
fix: logical; if TRUE, the covariance matrix is fixed to be positive semi-definite in case it is not.
use: character; specification passed to stats::cov() for handling missing coefficients/parameters.
.coef: a function used to extract the coefficients from each fitted model. Must return a numeric vector. By default, stats::coef is used, but marginaleffects::get_coef can be a more reliable choice for some models that have a non-standard coef() method, like that for nnet::multinom() models.
verbose: logical; whether to display a progress bar.
cl: a cluster object created by parallel::makeCluster(), or an integer to indicate the number of child-processes (integer values are ignored on Windows) for parallel evaluations. See pbapply::pblapply() for details. If NULL, no parallelization will take place.

Value

A matrix containing the covariance matrix estimate.

Details

vcovFWB() functions like other vcov()-like functions, such as those in the sandwich package, in particular, sandwich::vcovBS(), which implements the traditional bootstrap (and a few other bootstrap varieties for linear models). Sets of weights are generated as described in the documentation for fwb(), and the supplied model is re-fit using those weights. When the fitted model already has weights, these are multiplied by the bootstrap weights.

For lm objects, the model is re-fit using .lm.fit() for speed, and, similarly, glm objects are re-fit using glm.fit() (or whichever fitting method was originally used). For other objects, update() is used to populate the weights and re-fit the model (this assumes the fitting function accepts non-integer case weights through a weights argument). If a model accepts weights in some other way, fwb() should be used instead; vcovFWB() is inherently limited in its ability to handle all possible models. It is important that the original model was not fit using frequency weights (i.e., weights that allow one row of data to represent multiple full, identical, individual units).

See sandwich::vcovBS() and sandwich::vcovCL() for more information on clustering covariance matrices, and see fwb() for more information on how clusters work with the fractional weighted bootstrap. When clusters are specified, each cluster is given a bootstrap weight, and all members of the cluster are given that weight; estimation then proceeds as normal. By default, when cluster is unspecified, each unit is considered its own cluster.

Examples

set.seed(123)
data("infert")
fit <- glm(case ~ spontaneous + induced, data = infert,
             family = "binomial")
lmtest::coeftest(fit, vcov. = vcovFWB, R = 200)
#> 
#> z test of coefficients:
#> 
#>             Estimate Std. Error z value  Pr(>|z|)    
#> (Intercept) -1.70786    0.25592 -6.6734 2.500e-11 ***
#> spontaneous  1.19721    0.20314  5.8934 3.783e-09 ***
#> induced      0.41813    0.18206  2.2967   0.02164 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
# Example from help("vcovBS", package = "sandwich")
data("PetersenCL", package = "sandwich")
m <- lm(y ~ x, data = PetersenCL)

# Note: this is not to compare performance, just to
# demonstrate the syntax
cbind(
  "BS" = sqrt(diag(sandwich::vcovBS(m))),
  "FWB" = sqrt(diag(vcovFWB(m))),
  "BS-cluster" = sqrt(diag(sandwich::vcovBS(m, cluster = ~firm))),
  "FWB-cluster" = sqrt(diag(vcovFWB(m, cluster = ~firm)))
)
#>                     BS        FWB BS-cluster FWB-cluster
#> (Intercept) 0.02673669 0.02951612 0.06357961  0.06419107
#> x           0.02793417 0.02947605 0.04731831  0.04930975

# Using `wtype = "multinom"` exactly reproduces
# `sandwich::vcovBS()`
set.seed(11)
s <- sandwich::vcovBS(m, R = 200)
set.seed(11)
f <- vcovFWB(m, R = 200, wtype = "multinom")

all.equal(s, f)
#> [1] TRUE
# Using a custom argument to `.coef`
set.seed(123)
data("infert")

fit <- nnet::multinom(education ~ age, data = infert,
                      trace = FALSE)

# vcovFWB(fit, R = 200) ## error
coef(fit) # coef() returns a matrix
#>         (Intercept)         age
#> 6-11yrs    5.482932 -0.09335993
#> 12+ yrs    9.372401 -0.21892472

# Write a custom function to extract vector of
# coefficients (can also use marginaleffects::get_coef())
coef_multinom <- function(x) {
  p <- t(coef(x))

  setNames(as.vector(p),
           paste(colnames(p)[col(p)],
                 rownames(p)[row(p)],
                 sep = ":"))
}
coef_multinom(fit) # returns a vector
#> 6-11yrs:(Intercept)         6-11yrs:age 12+ yrs:(Intercept)         12+ yrs:age 
#>          5.48293157         -0.09335993          9.37240097         -0.21892472 

vcovFWB(fit, R = 200, .coef = coef_multinom)
#>                     6-11yrs:(Intercept)  6-11yrs:age 12+ yrs:(Intercept)
#> 6-11yrs:(Intercept)           8.4430557 -0.235078549           8.1517264
#> 6-11yrs:age                  -0.2350785  0.006628142          -0.2265586
#> 12+ yrs:(Intercept)           8.1517264 -0.226558550           8.6180355
#> 12+ yrs:age                  -0.2261878  0.006360024          -0.2410550
#>                      12+ yrs:age
#> 6-11yrs:(Intercept) -0.226187847
#> 6-11yrs:age          0.006360024
#> 12+ yrs:(Intercept) -0.241054977
#> 12+ yrs:age          0.006827831