# boot_ci: Confidence Intervals from Bootstrapped Network Degree... In snowboot: Bootstrap Methods for Network Inference

## Description

The function calculates bootstrap confidence intervals for the parameters of network degree distribution: probabilities of node degrees f(k) and mean degree μ, where k = 0, 1, … are the degrees.

## Usage

 1 boot_ci(x, prob = 0.95, method = c("percentile", "basic")) 

## Arguments

 x a list with bootstrapped results – output of boot_dd. prob confidence level for the intervals. Default is 0.95 (i.e., 95% confidence). method method for calculating the bootstrap intervals. Default is "percentile" (see Details).

## Details

Currently, the bootstrap intervals can be calculated with two alternative methods: "percentile" or "basic". The "percentile" intervals correspond to Efron's 100\cdotprob% intervals \insertCite@see @efron_1979, also Equation 5.18 by @davison_hinkley_1997 and Equation 3 by @gel_etal_2017, @chen_etal_2018_snowbootsnowboot:

(θ^*_{[Bα/2]}, θ^*_{[B(1-α/2)]}),

where θ^*_{[Bα/2]} and θ^*_{[B(1-α/2)]} are empirical quantiles of the bootstrap distribution with B bootstrap replications for parameter θ (θ can be the f(k) or μ), and α = 1 - prob.

The "basic" method produces intervals \insertCite@see Equation 5.6 by @davison_hinkley_1997snowboot:

(2\hat{θ} - θ^*_{[B(1-α/2)]}, 2\hat{θ} - θ^*_{[Bα/2]}),

where \hat{θ} is the sample estimate of the parameter. Note that this method can lead to negative confidence bounds, especially when \hat{θ} is close to 0.

## Value

A list object of class "snowboot" with the following elements:

 fk_ci A matrix of dimensions 2 \timeslength(x$fk), where the number of columns corresponds to the number of probabilities f(k) estimated from an LSMI sample. Each column of the matrix is a confidence interval for a corresponding f(k). I.e., the first row of the matrix gives the lower bounds, while the second row contains all upper bounds. mu_ci A numeric vector of length 2 with lower and upper confidence bounds for the network mean degree μ. prob Confidence level for the intervals. method Method that was used for calculating the bootstrap intervals. fk A vector with an estimate of the degree distribution, copied from the input x$fk. mu An estimate of the mean degree, copied from the input x\$mu.

## References

\insertAllCited

boot_dd
 1 2 3 4 5 6 7 net <- artificial_networks[[1]] lsmiEstimate <- lsmi_dd(net = net, n.seed = 5, n.wave = 3) bootEstimates <- boot_dd(lsmiEstimate, B = 10) bootIntervals1 <- boot_ci(bootEstimates) #Another version of the intervals: bootIntervals2 <- boot_ci(bootEstimates, method = "basic")