Summarize fwb Output — summary.fwb • fwb

summary() creates a regression summary-like table that displays the bootstrap estimates, their empirical standard errors, their confidence intervals, and, optionally, p-values for tests against a null value. confint() produces just the confidence intervals, and is called internally by summary().

Usage

# S3 method for class 'fwb'
summary(
  object,
  conf = 0.95,
  ci.type = "bc",
  p.value = FALSE,
  index = seq_len(ncol(object$t)),
  null = 0,
  simultaneous = FALSE,
  ...
)

# S3 method for class 'fwb'
confint(object, parm, level = 0.95, ci.type = "bc", simultaneous = FALSE, ...)

Arguments

object: an fwb object; the output of a call to fwb().
conf, level: the desired confidence level. Default is .95 for 95% confidence intervals. Set to 0 to prevent calculation of confidence intervals.
ci.type: the type of confidence interval desired. Allowable options include "wald" (Wald interval), "norm" (normal approximation), "basic" (basic interval), "perc" (percentile interval), "bc" (bias-corrected percentile interval), and "bca" (bias-corrected and accelerated [BCa] interval). Only one is allowed. BCa intervals require the number of bootstrap replications to be larger than the sample size. See fwb.ci() for details. The default is "bc". Ignored if both conf = 0 and p.values = FALSE.
p.value: logical; whether to display p-values for the test that each parameter is equal to null. Default is FALSE. See Details.
index, parm: the index or indices of the position of the quantity of interest if more than one was specified in fwb(). Default is to display all quantities.
null: numeric; when p.value = TRUE, the value of the estimate under the null hypothesis. Default is 0. Only one value can be supplied and it is applied to all tests.
simultaneous: logical; whether to adjust confidence intervals and p-values to ensure correct familywise coverage/size across all specified estimates. See Details. Default is FALSE for standard pointwise intervals. TRUE is only allowed when ci.type is "wald" or "perc".
...: ignored.

Value

For summary(), a summary.fwb object, which is a matrix with the following columns:

Estimate: the statistic estimated in the original sample
Std. Error: the standard deviation of the bootstrap estimates
CI {L}% and CI {U}%: the upper and lower confidence interval bounds computed using the argument to ci.type (only when conf is not 0).
z value: when p.value = TRUE and ci.type = "wald", the z-statistic for the test of the estimate against against null.
Pr(>|z|): when p.value = TRUE, the p-value for the test of the estimate against against null.

For confint(), a matrix with a row for each statistic and a column for the upper and lower confidence interval limits.

Details

P-values are computed by inverting the confidence interval for each parameter, i.e., finding the largest confidence level yielding a confidence interval that excludes null, and taking the p-value to be one minus that level. This ensures conclusions from tests based on the p-value and whether the confidence interval contains the null value always yield the same conclusion. Prior to version 0.5.0, all p-values were based on inverting Wald confidence intervals, regardless of ci.type.

Simultaneous confidence intervals are computed using the "sup-t" confidence band, which involves modifying the confidence level so that the intersection of all the adjusted confidence intervals contain the whole parameter vector with the specified coverage. This will always be less conservative than Bonferroni or Holm adjustment. See Olea and Plagborg-Møller (2019) for details on implementation for Wald and percentile intervals. Simultaneous p-values are computed by inverting the simultaneous bands. Simultaneous inference is only allowed when ci.type is "wald" or "perc" and index has length greater than 1. When ci.type = "wald", the mvtnorm package must be installed.

tidy() and print() methods are available for summary.fwb objects.

References

Montiel Olea, J. L., & Plagborg-Møller, M. (2019). Simultaneous confidence bands: Theory, implementation, and an application to SVARs. Journal of Applied Econometrics, 34(1), 1–17. doi:10.1002/jae.2656

Examples

set.seed(123, "L'Ecuyer-CMRG")
data("infert")

fit_fun <- function(data, w) {
  fit <- glm(case ~ spontaneous + induced, data = data,
             family = "quasibinomial", weights = w)
  coef(fit)
}

fwb_out <- fwb(infert, fit_fun, R = 199,
               verbose = FALSE)

# Basic confidence interval for both estimates
summary(fwb_out, ci.type = "basic")
#>             Estimate Std. Error CI 2.5 % CI 97.5 %
#> (Intercept)  -1.7079     0.2647  -2.2118   -1.2074
#> spontaneous   1.1972     0.2185   0.7532    1.6483
#> induced       0.4181     0.1975   0.0331    0.8116

# Just for "induced" coefficient; p-values requested,
# no confidence intervals
summary(fwb_out, ci.type = "norm", conf = 0,
        index = "induced", p.value = TRUE)
#>         Estimate Std. Error Pr(>|z|)  
#> induced    0.418      0.197    0.035 *
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Summarize `fwb` Output