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

Description Usage Arguments Details Value References See Also Examples

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.

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

`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).

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.

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

`fk_ci`	A matrix of dimensions 2 \times`length(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`.

\insertAllCited

boot_dd

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")