networkscaleup (version 0.2-1)

killworth: Fit Killworth models to ARD. This function estimates the degrees and population sizes using the plug-in MLE and MLE estimator.

Description

Fit Killworth models to ARD. This function estimates the degrees and population sizes using the plug-in MLE and MLE estimator.

Usage

killworth(
  ard,
  known_sizes = NULL,
  known_ind = 1:length(known_sizes),
  N = NULL,
  model = c("MLE", "PIMLE")
)

Value

A named list with the estimated degrees and sizes.

Arguments

ard

The `n_i x n_k` matrix of non-negative ARD integer responses, where the `(i,k)th` element corresponds to the number of people that respondent `i` knows in subpopulation `k`.

known_sizes

The known subpopulation sizes corresponding to a subset of the columns of ard.

known_ind

The indices that correspond to the columns of ard with known_sizes. By default, the function assumes the first n_known columns, where n_known corresponds to the number of known_sizes.

N

The known total population size.

model

A character string corresponding to either the plug-in MLE (PIMLE) or the MLE (MLE). The function assumes MLE by default.

References

Killworth, P. D., Johnsen, E. C., McCarty, C., Shelley, G. A., and Bernard, H. R. (1998). A Social Network Approach to Estimating Seroprevalence in the United States, Social Networks, 20, 23--50

Killworth, P. D., McCarty, C., Bernard, H. R., Shelley, G. A., and Johnsen, E. C. (1998). Estimation of Seroprevalence, Rape and Homelessness in the United States Using a Social Network Approach, Evaluation Review, 22, 289--308

Laga, I., Bao, L., and Niu, X. (2021). Thirty Years of the Network Scale-up Method, Journal of the American Statistical Association, 116:535, 1548--1559

Examples

# Analyze an example ard data set using the killworth function
data(example_data)

ard <- example_data$ard
subpop_sizes <- example_data$subpop_sizes
N <- example_data$N

mle.est <- killworth(ard,
  known_sizes = subpop_sizes[c(1, 2, 4)],
  known_ind = c(1, 2, 4),
  N = N, model = "MLE"
)

pimle.est <- killworth(ard,
  known_sizes = subpop_sizes[c(1, 2, 4)],
  known_ind = c(1, 2, 4),
  N = N, model = "PIMLE"
)

## Compare estimates with the truth
plot(mle.est$degrees, example_data$degrees)

data.frame(
  true = subpop_sizes[c(3, 5)],
  mle = mle.est$sizes,
  pimle = pimle.est$sizes
)