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

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")
)

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.

Value

A named list with the estimated degrees and sizes.

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"
)
#> Warning: Estimated a 0 degree for at least one respondent. Ignoring response for 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
)
#>    true      mle    pimle
#> 1 36246 34976.60 31232.11
#> 2 20174 20042.77 20831.44