Description Usage Arguments Details Value References See Also Examples
From the vector of specified n.seeds
and possible waves 1:n.wave
around each
seed, the function selects a single number n.seed
and an n.wave
(optimal seed-wave combination) that produce
a labeled snowball with multiple inclusions (LSMI) sample with desired
bootstrap confidence intervals for a parameter of interest. Here by ‘desired’
we mean that the interval (and corresponding seed-wave combination) are selected
as having the best coverage (closest to the specified level prob
), based on
a cross-validation procedure with proxy estimates of the parameter.
See Algorithm 2 by \insertCitegel_etal_2017;textualsnowboot and Details
below.
1 2 3 4 5 6 7 8 9 10 11 12 13 |
net |
a network object that is a list containing:
The network object can be simulated by |
n.seeds |
an integer vector of numbers of seeds for snowball sampling
(cf. a single integer |
n.wave |
an integer defining the number of waves (order of the neighborhood)
to be recorded around the seed in the LSMI. For example, |
seeds |
a vector of numeric IDs of pre-specified seeds. If specified, LSMIs are constructed around each such seed. |
B |
a positive integer, the number of bootstrap replications to perform. Default is 100. |
prob |
confidence level for the intervals. Default is 0.95 (i.e., 95% confidence). |
cl |
parameter to specify computer cluster for bootstrapping, passed to
the package
|
param |
The parameter of interest for which to run a cross-validation
and select optimal |
method |
method for calculating the bootstrap intervals. Default is
|
proxyRep |
The number of times to repeat proxy sampling. Default is 19. |
proxySize |
The size of the proxy sample. Default is 30. |
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 consisting of:
bci |
A numeric vector of length 2 with the bootstrap confidence interval
(lower bound, upper bound) for the parameter of interest. This interval is
obtained by bootstrapping node degrees in an LSMI with the optimal combination
of |
estimate |
Point estimate of the parameter of interest
(based on the LSMI with |
best_combination |
An integer vector of lenght 2 containing the optimal
|
seeds |
A vector of numeric IDs of the seeds that were used
in the LSMI with the optimal combination of |
lsmi
, lsmi_union
, boot_dd
, boot_ci
1 2 | net <- artificial_networks[[1]]
a <- lsmi_cv(net, n.seeds = c(10, 20, 30), n.wave = 5, B = 100)
|
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