| Title: | Network Scale-Up Models for Aggregated Relational Data |
| Version: | 0.2-1 |
| Description: | Provides a variety of Network Scale-up Models for researchers to analyze Aggregated Relational Data, through the use of Stan and 'glmmTMB'. Also provides tools for model checking In this version, the package implements models from Laga, I., Bao, L., and Niu, X (2023) <doi:10.1080/01621459.2023.2165929>, Zheng, T., Salganik, M. J., and Gelman, A. (2006) <doi:10.1198/016214505000001168>, Killworth, P. D., Johnsen, E. C., McCarty, C., Shelley, G. A., and Bernard, H. R. (1998) <doi:10.1016/S0378-8733(96)00305-X>, and Killworth, P. D., McCarty, C., Bernard, H. R., Shelley, G. A., and Johnsen, E. C. (1998) <doi:10.1177/0193841X9802200205>. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Biarch: | true |
| Depends: | R (≥ 4.1.0) |
| Imports: | methods, Rcpp (≥ 0.12.0), rstan (≥ 2.26.0), LaplacesDemon (≥ 16.1.6), dplyr, ggplot2, scales, stats, readr, tibble, tidyr, graphics, rlang, glmmTMB, gridExtra, purrr, stringr, trialr, tidyselect, RMTstat |
| LinkingTo: | BH (≥ 1.66.0), Rcpp (≥ 0.12.0), RcppEigen (≥ 0.3.3.3.0), rstan (≥ 2.26.0), StanHeaders (≥ 2.26.0) |
| SystemRequirements: | GNU make |
| Suggests: | rmarkdown, knitr |
| VignetteBuilder: | knitr |
| LazyData: | true |
| NeedsCompilation: | yes |
| Packaged: | 2025-12-10 16:27:17 UTC; ianlaga |
| Author: | Ian Laga  [aut,
cre],
Owen G. Ward [aut],
Anna L. Smith [aut],
Benjamin Vogel [aut],
Jieyun Wang [aut],
Le Bao [aut],
Xiaoyue Niu [aut] |
| Maintainer: | Ian Laga <ilaga25@gmail.com> |
| URL: | https://github.com/ilaga/networkscaleup |
| Repository: | CRAN |
| Date/Publication: | 2025-12-10 18:40:02 UTC |
The 'networkscaleup' package.
Description
Provides a variety of Network Scale-up Models for researchers to analyze Aggregated Relational Data, mostly through the use of Stan.
Author(s)
Maintainer: Ian Laga ilaga25@gmail.com (ORCID)
Authors:
Owen G. Ward oward@sfu.ca
Anna L. Smith
Benjamin Vogel
Jieyun Wang
Le Bao lebao@psu.edu
Xiaoyue Niu Xiaoyue@psu.edu
See Also
Useful links:
Compute Pearson Residuals for ARD matrix and fitted model
Description
Compute Pearson Residuals for ARD matrix and fitted model
Usage
construct_pearson(ard, model_fit)
Arguments
ard |
ARD matrix y |
model_fit |
estimated model |
Value
a vector (column by column) of corresponding residuals from ARD matrix
Compute Randomized Quantile Residuals for ARD Models
Description
Compute Randomized Quantile Residuals for ARD Models
Usage
construct_rqr(ard, model_fit)
Arguments
ard |
ard matrix |
model_fit |
fitted model, along with required details |
Value
a vector of residuals (column by column)
Fit ARD using the uncorrelated or correlated model in Stan This function fits the ARD using either the uncorrelated or correlated model in Laga et al. (2021) in Stan. The population size estimates and degrees are scaled using a post-hoc procedure.
Description
Fit ARD using the uncorrelated or correlated model in Stan This function fits the ARD using either the uncorrelated or correlated model in Laga et al. (2021) in Stan. The population size estimates and degrees are scaled using a post-hoc procedure.
Usage
correlatedStan(
ard,
known_sizes = NULL,
known_ind = NULL,
N = NULL,
model = c("correlated", "uncorrelated"),
scaling = c("all", "overdispersed", "weighted", "weighted_sq"),
x = NULL,
z_global = NULL,
z_subpop = NULL,
G1_ind = NULL,
G2_ind = NULL,
B2_ind = NULL,
chains = 3,
cores = 1,
warmup = 1000,
iter = 1500,
thin = 1,
return_fit = FALSE,
...
)
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 |
known_ind |
The indices that correspond to the columns of |
N |
The known total population size. |
model |
A character vector denoting which of the two models should be fit, either 'uncorrelated' or 'correlated'. More details of these models are provided below. The function decides which covariate model is needed based on the covariates provided below. |
scaling |
An optional character vector providing the name of scaling procedure should be performed in order to transform estimates to degrees and subpopulation sizes. If 'NULL', the parameters will be returned unscaled. Alternatively, scaling may be performed independently using the scaling function. Scaling options are 'NULL', 'overdispersed', 'all', 'weighted', or 'weighted_sq' ('weighted' and 'weighted_sq' are only available if 'model = "correlated"'. Further details are provided in the Details section. |
x |
A matrix with dimensions 'n_i x n_unknown', where 'n_unknown' refers to the number of unknown subpopulation sizes. In the language of Teo et al. (2019), these represent the individual's perception of each hidden population. |
z_global |
A matrix with dimensions 'n_i x p_global', where 'p_global' is the number of demographic covariates used. This matrix represents the demographic information about the respondents in order to capture the barrier effects. |
z_subpop |
A matrix with dimensions 'n_i x p_subpop', where 'p_subpop' is the number of demographic covariates used. This matrix represents the demographic information about the respondents in order to capture the barrier effects. |
G1_ind |
A vector of indices denoting the columns of 'ard' that correspond to the primary scaling groups, i.e. the collection of rare girls' names in Zheng, Salganik, and Gelman (2006). By default, all known_sizes are used. If G2_ind and B2_ind are not provided, 'C = C_1', so only G1_ind are used. If G1_ind is not provided, no scaling is performed. |
G2_ind |
A vector of indices denoting the columns of 'ard' that correspond to the subpopulations that belong to the first secondary scaling groups, i.e. the collection of somewhat popular girls' names. |
B2_ind |
A vector of indices denoting the columns of 'ard' that correspond to the subpopulations that belong to the second secondary scaling groups, i.e. the collection of somewhat popular boys' names. |
chains |
A positive integer specifying the number of Markov chains. |
cores |
A positive integer specifying the number of cores to use to run the Markov chains in parallel. |
warmup |
A positive integer specifying the total number of samples for each chain (including warmup). Matches the usage in stan. |
iter |
A positive integer specifying the number of warmup samples for each chain. Matches the usage in stan. |
thin |
A positive integer specifying the interval for saving posterior samples. Default value is 1 (i.e. no thinning). |
return_fit |
A logical indicating whether the fitted 'stanfit' object should be return. Defaults to 'FALSE'. |
... |
Additional arguments to be passed to stan. |
Details
This function currently fits a variety of models proposed in Laga et al. (2022+). The user may provide any combination of 'x', 'z_global', and 'z_subpop'. Additionally, the user may choose to fit a uncorrelated version of the model, where the correlation matrix is equal to the identity matrix.
The 'scaling' options are described below:
- NULL
No scaling is performed
- overdispersed
The scaling procedure outlined in Zheng et al. (2006) is performed. In this case, at least 'Pg1_ind' must be provided. See overdispersedStan for more details.
- all
All subpopulations with known sizes are used to scale the parameters, using a modified scaling procedure that standardizes the sizes so each population is weighted equally. Additional details are provided in Laga et al. (2022+).
- weighted
All subpopulations with known sizes are weighted according their correlation with the unknown subpopulation size. Additional details are provided in Laga et al. (2022+)
- weighted_sq
Same as 'weighted', except the weights are squared, providing more relative weight to subpopulations with higher correlation.
Value
Either the full fitted Stan model if return_fit = TRUE, else a
named list with the estimated parameters extracted using
extract (the default). The estimated parameters are named as
follows (if estimated in the corresponding model), with additional
descriptions as needed:
- delta
Raw delta parameters
- sigma_delta
Standard deviation of delta
- rho
Log prevalence, if scaled, else raw rho parameters
- mu_rho
Mean of rho
- sigma_rho
Standard deviation of rho
- alpha
Slope parameters corresponding to z
- beta_global
Slope parameters corresponding to x_global
- beta_subpop
Slope parameters corresponding to x_subpop
- tau_N
Standard deviation of random effects b
- Corr
Correlation matrix, if 'Correlation = TRUE'
If scaled, the following additional parameters are included:
- log_degrees
Scaled log degrees
- degree
Scaled degrees
- log_prevalences
Scaled log prevalences
- sizes
Subpopulation size estimates
References
Laga, I., Bao, L., and Niu, X (2021). A Correlated Network Scaleup Model: Finding the Connection Between Subpopulations
Examples
## Not run:
data(example_data)
x <- example_data$x
z_global <- example_data$z[, 1:2]
z_subpop <- example_data$z[, 3:4]
basic_corr_est <- correlatedStan(example_data$ard,
known_sizes = example_data$subpop_sizes[c(1, 2, 4)],
known_ind = c(1, 2, 4),
N = example_data$N,
model = "correlated",
scaling = "weighted",
chains = 1,
cores = 1,
warmup = 50,
iter = 100
)
cov_uncorr_est <- correlatedStan(example_data$ard,
known_sizes = example_data$subpop_sizes[c(1, 2, 4)],
known_ind = c(1, 2, 4),
N = example_data$N,
model = "uncorrelated",
scaling = "all",
x = x,
z_global = z_global,
z_subpop = z_subpop,
chains = 1,
cores = 1,
warmup = 50,
iter = 100
)
cov_corr_est <- correlatedStan(example_data$ard,
known_sizes = example_data$subpop_sizes[c(1, 2, 4)],
known_ind = c(1, 2, 4),
N = example_data$N,
model = "correlated",
scaling = "all",
x = x,
z_subpop = z_subpop,
chains = 1,
cores = 1,
warmup = 50,
iter = 100
)
# Compare size estimates
round(data.frame(
true = example_data$subpop_sizes,
corr_basic = colMeans(basic_corr_est$sizes),
uncorr_x_zsubpop_zglobal = colMeans(cov_uncorr_est$sizes),
corr_x_zsubpop = colMeans(cov_corr_est$sizes)
))
# Look at z slope parameters
colMeans(cov_uncorr_est$beta_global)
colMeans(cov_corr_est$beta_subpop)
colMeans(cov_uncorr_est$beta_subpop)
# Look at x slope parameters
colMeans(cov_uncorr_est$alpha)
colMeans(cov_corr_est$alpha)
## End(Not run)
Covariance plots
Description
Plots of the estimated covariance structure from a given fitted model
Usage
cov_plots(
ard,
model_fit,
x_cov,
resid_type = c("rqr", "pearson_residuals"),
method = "lm",
se = F
)
Arguments
ard |
ard matrix |
model_fit |
a fitted object from [fit_mle()] or [fit_map()] |
x_cov |
covariate matrix |
resid_type |
the type of residuals to use |
method |
the method to use |
se |
whether to compute standard errors of estimates |
Value
a list of ggplots, corresponding to covariance structure
Dispersion Metric for Fitted ARD Model
Description
Dispersion Metric for Fitted ARD Model
Usage
dispersion_metric(ard, model_fit)
Arguments
ard |
ard matrix |
model_fit |
list of fitted model and details |
Value
a ggplot of the hanging rootogram
Simulated ARD data set with z and x.
Description
A simulated data set to demonstrate and test the NSUM methods. The data was simulated from the basic Killworth Binomial model.
Usage
example_data
Format
A named list for an ARD survey from 100 respondents about 5 subpopulations.
- ard
A '100 x 5' matrix with integer valued respondents
- x
A '100 x 5' matrix with simulated answers from a 1-5 Likert scale
- z
A '100 x 4' matrix with answers for each respondents about 4 demographic questions
- N
An integer specifying the total population size
- subpop_size
A vector with the 5 true subpopulation sizes
- degrees
A vector with the 100 true respondent degrees
Fit basic Poisson and Negative Binomial models using glmmTMB
Description
Fit basic Poisson and Negative Binomial models using glmmTMB
Usage
fit_mle(
ard,
x_cov_global = NULL,
x_cov_local = NULL,
family = c("poisson", "nbinomial")
)
Arguments
ard |
n_i by n_k ARD matrix |
x_cov_global |
n_i by p_global covariate matrix of global covariates |
x_cov_local |
n_i by p_local covariate matrix of local covariates |
family |
distribution to fit, either "poisson" or "nbinomial" |
Value
list containing fitted model and extracted parameters
Compute Surrogate Residuals for ARD Models
Description
Compute Surrogate Residuals for ARD Models
Usage
get_surrogate(ard, model_fit = NULL)
Arguments
ard |
the ARD matrix |
model_fit |
list containing fitted model, details |
Value
a vector of residuals (column by column)
Hanging Rootogram for Fitted ARD Model
Description
Hanging Rootogram for Fitted ARD Model
Usage
hang_rootogram_ard(ard, model_fit, width = 0.9, x_max = NULL, by_group = FALSE)
Arguments
ard |
ard matrix |
model_fit |
fitted model object |
width |
width of bars |
x_max |
the maximum x value to display |
by_group |
logical; if TRUE, create separate rootograms for each column (group) |
Value
a ggplot of the hanging rootogram (single plot if by_group=FALSE, combined plot if by_group=TRUE)
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")
)
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 |
known_ind |
The indices that correspond to the columns of |
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"
)
## 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
)
log computed uniform quantile
Description
log computed uniform quantile
Usage
log_mix_uniform(logFl, logFu)
Arguments
logFl |
log of lower value |
logFu |
log of upper value |
Value
log value of uniform between Flower and Fupper
Generate simulated ARD
Description
Generate simulated ARD
Usage
make_ard(
n_i = 500,
n_k = 20,
N = 1e+06,
p = 0,
p_global_nonzero = 0,
p_local_nonzero = 0,
group_corr = FALSE,
degree_corr = FALSE,
family = c("poisson", "nbinomial"),
omega_range = c(1, 5),
alpha_mean = 5,
alpha_sd = 0.15,
eta = 3,
seed = NULL
)
Arguments
n_i |
number of respondents (rows) |
n_k |
number of groups (columns) |
N |
total population size |
p |
number of collected covariates |
p_global_nonzero |
number of non-zero global covariates |
p_local_nonzero |
number of non-zero local covariates |
group_corr |
group correlation |
degree_corr |
degree correlation |
family |
sampling distribution |
omega_range |
minimum and maximum omega for negative binomial overdispersion |
alpha_mean |
mean of alphas |
alpha_sd |
variance of alphas |
eta |
correlation hyperparameter for LKJ prior |
seed |
random seed |
Value
simulated ARD along with all true parameters
Examples
make_ard(N = 10000, family = "poisson")
Construct tibble from ARD matrix
Description
Construct tibble from ARD matrix
Usage
make_ard_tidy(ard)
Arguments
ard |
the ARD matrix |
Value
a tibble of ARD, with columns for row/col index
Fit Overdispersed model to ARD (Gibbs-Metropolis)
Description
This function fits the ARD using the Overdispersed model using the original Gibbs-Metropolis Algorithm provided in Zheng, Salganik, and Gelman (2006). The population size estimates and degrees are scaled using a post-hoc procedure. For the Stan implementation, see overdispersedStan.
Usage
overdispersed(
ard,
known_sizes = NULL,
known_ind = NULL,
G1_ind = NULL,
G2_ind = NULL,
B2_ind = NULL,
N = NULL,
warmup = 1000,
iter = 1500,
refresh = NULL,
thin = 1,
verbose = FALSE,
alpha_tune = 0.4,
beta_tune = 0.2,
omega_tune = 0.2,
init = "MLE"
)
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 |
known_ind |
The indices that correspond to the columns of |
G1_ind |
A vector of indices denoting the columns of 'ard' that correspond to the primary scaling groups, i.e. the collection of rare girls' names in Zheng, Salganik, and Gelman (2006). By default, all known_sizes are used. If G2_ind and B2_ind are not provided, 'C = C_1', so only G1_ind are used. If G1_ind is not provided, no scaling is performed. |
G2_ind |
A vector of indices denoting the columns of 'ard' that correspond to the subpopulations that belong to the first secondary scaling groups, i.e. the collection of somewhat popular girls' names. |
B2_ind |
A vector of indices denoting the columns of 'ard' that correspond to the subpopulations that belong to the second secondary scaling groups, i.e. the collection of somewhat popular boys' names. |
N |
The known total population size. |
warmup |
A positive integer specifying the number of warmup samples. |
iter |
A positive integer specifying the total number of samples (including warmup). |
refresh |
An integer specifying how often the progress of the sampling
should be reported. By default, resorts to every 10
|
thin |
A positive integer specifying the interval for saving posterior samples. Default value is 1 (i.e. no thinning). |
verbose |
Logical value, specifying whether sampling progress should be reported. |
alpha_tune |
A positive numeric indicating the standard deviation used as the jumping scale in the Metropolis step for alpha. Defaults to 0.4, which has worked well for other ARD datasets. |
beta_tune |
A positive numeric indicating the standard deviation used as the jumping scale in the Metropolis step for beta Defaults to 0.2, which has worked well for other ARD datasets. |
omega_tune |
A positive numeric indicating the standard deviation used as the jumping scale in the Metropolis step for omega Defaults to 0.2, which has worked well for other ARD datasets. |
init |
A named list with names corresponding to the first-level model
parameters, name 'alpha', 'beta', and 'omega'. By default the 'alpha' and
'beta' parameters are initialized at the values corresponding to the
Killworth MLE estimates (for the missing 'beta'), with all 'omega' set to
20. Alternatively, |
Details
This function fits the overdispersed NSUM model using the Metropolis-Gibbs sampler provided in Zheng et al. (2006).
Value
A named list with the estimated posterior samples. The estimated parameters are named as follows, with additional descriptions as needed:
- alphas
Log degree, if scaled, else raw alpha parameters
- betas
Log prevalence, if scaled, else raw beta parameters
- inv_omegas
Inverse of overdispersion parameters
- sigma_alpha
Standard deviation of alphas
- mu_beta
Mean of betas
- sigma_beta
Standard deviation of betas
- omegas
Overdispersion parameters
If scaled, the following additional parameters are included:
- mu_alpha
Mean of log degrees
- degrees
Degree estimates
- sizes
Subpopulation size estimates
References
Zheng, T., Salganik, M. J., and Gelman, A. (2006). How many people do you know in prison, Journal of the American Statistical Association, 101:474, 409–423
Examples
# Analyze an example ard data set using Zheng et al. (2006) models
# Note that in practice, both warmup and iter should be much higher
data(example_data)
ard <- example_data$ard
subpop_sizes <- example_data$subpop_sizes
known_ind <- c(1, 2, 4)
N <- example_data$N
overdisp.est <- overdispersed(ard,
known_sizes = subpop_sizes[known_ind],
known_ind = known_ind,
G1_ind = 1,
G2_ind = 2,
B2_ind = 4,
N = N,
warmup = 50,
iter = 100
)
# Compare size estimates
data.frame(
true = subpop_sizes,
basic = colMeans(overdisp.est$sizes)
)
# Compare degree estimates
plot(example_data$degrees, colMeans(overdisp.est$degrees))
# Look at overdispersion parameter
colMeans(overdisp.est$omegas)
Fit ARD using the Overdispersed model in Stan
Description
This function fits the ARD using the Overdispersed model in Stan. The population size estimates and degrees are scaled using a post-hoc procedure. For the Gibbs-Metropolis algorithm implementation, see overdispersed.
Usage
overdispersedStan(
ard,
known_sizes = NULL,
known_ind = NULL,
G1_ind = NULL,
G2_ind = NULL,
B2_ind = NULL,
N = NULL,
chains = 3,
cores = 1,
warmup = 1000,
iter = 1500,
thin = 1,
return_fit = FALSE,
...
)
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 |
known_ind |
The indices that correspond to the columns of |
G1_ind |
A vector of indices denoting the columns of 'ard' that correspond to the primary scaling groups, i.e. the collection of rare girls' names in Zheng, Salganik, and Gelman (2006). By default, all known_sizes are used. If G2_ind and B2_ind are not provided, 'C = C_1', so only G1_ind are used. If G1_ind is not provided, no scaling is performed. |
G2_ind |
A vector of indices denoting the columns of 'ard' that correspond to the subpopulations that belong to the first secondary scaling groups, i.e. the collection of somewhat popular girls' names. |
B2_ind |
A vector of indices denoting the columns of 'ard' that correspond to the subpopulations that belong to the second secondary scaling groups, i.e. the collection of somewhat popular boys' names. |
N |
The known total population size. |
chains |
A positive integer specifying the number of Markov chains. |
cores |
A positive integer specifying the number of cores to use to run the Markov chains in parallel. |
warmup |
A positive integer specifying the total number of samples for each chain (including warmup). Matches the usage in stan. |
iter |
A positive integer specifying the number of warmup samples for each chain. Matches the usage in stan. |
thin |
A positive integer specifying the interval for saving posterior samples. Default value is 1 (i.e. no thinning). |
return_fit |
A logical indicating whether the fitted Stan model should be returned instead of the rstan::extracted and scaled parameters. This is FALSE by default. |
... |
Additional arguments to be passed to stan. |
Details
This function fits the overdispersed NSUM model using the Gibbs-Metropolis algorithm provided in Zheng et al. (2006).
Value
Either the full fitted Stan model if return_fit = TRUE, else a
named list with the estimated parameters extracted using
extract (the default). The estimated parameters are named as
follows, with additional descriptions as needed:
- alphas
Log degree, if 'scaling = TRUE', else raw alpha parameters
- betas
Log prevalence, if 'scaling = TRUE', else raw beta parameters
- inv_omegas
Inverse of overdispersion parameters
- sigma_alpha
Standard deviation of alphas
- mu_beta
Mean of betas
- sigma_beta
Standard deviation of betas
- omegas
Overdispersion parameters
If 'scaling = TRUE', the following additional parameters are included:
- mu_alpha
Mean of log degrees
- degrees
Degree estimates
- sizes
Subpopulation size estimates
References
Zheng, T., Salganik, M. J., and Gelman, A. (2006). How many people do you know in prison, Journal of the American Statistical Association, 101:474, 409–423
Examples
# Analyze an example ard data set using Zheng et al. (2006) models
# Note that in practice, both warmup and iter should be much higher
## Not run:
data(example_data)
ard <- example_data$ard
subpop_sizes <- example_data$subpop_sizes
known_ind <- c(1, 2, 4)
N <- example_data$N
overdisp.est <- overdispersedStan(ard,
known_sizes = subpop_sizes[known_ind],
known_ind = known_ind,
G1_ind = 1,
G2_ind = 2,
B2_ind = 4,
N = N,
chains = 1,
cores = 1,
warmup = 250,
iter = 500
)
# Compare size estimates
round(data.frame(
true = subpop_sizes,
basic = colMeans(overdisp.est$sizes)
))
# Compare degree estimates
plot(example_data$degrees, colMeans(overdisp.est$degrees))
# Look at overdispersion parameter
colMeans(overdisp.est$omegas)
## End(Not run)
Plot residuals against fitted values
Description
Plot residuals against fitted values
Usage
plot_fitted(ard, model_fit = NULL, resid = c("rqr", "pearson", "surrogate"))
Arguments
ard |
ARD matrix (may be needed) |
model_fit |
fitted model |
resid |
the type of residuals to be used |
Value
a ggplot showing fitted values against residuals
Construction Residual (row/column) correlation matrix
Description
Construction Residual (row/column) correlation matrix
Usage
residual_correlation(ard_residuals, ard, type = "column")
Arguments
ard_residuals |
vector of residuals |
ard |
ard matrix |
type |
type of correlation to use (row or column) |
Value
a ggplot of the specified correlation matrix
Construct heatmap of residuals
Description
Construct heatmap of residuals
Usage
residual_heatmap(ard_residuals, ard)
Arguments
ard_residuals |
a vector (column wise) of estimated residuals |
ard |
an ard matrix |
Value
A ggplot of residual heatmap
compute numerically stable negative binomial rqr
Description
compute numerically stable negative binomial rqr
Usage
rqr_nbinom_logs(y, size, prob, eps = 1e-12)
Arguments
y |
observed value |
size |
size parameter |
prob |
prob parameter |
eps |
precision parameter |
Value
appropriate randomized quantile residual
compute numerically stable Poisson rqr
Description
compute numerically stable Poisson rqr
Usage
rqr_pois_logs(y, mu, eps = 1e-12)
Arguments
y |
observed value |
mu |
mean value of poisson |
eps |
precision parameter |
Value
appropriate randomized quantile residual
Scale raw log degree and log prevalence estimates
Description
This function scales estimates from either the overdispersed model or from the correlated models. Several scaling options are available.
Usage
scaling(
log_degrees,
log_prevalences,
scaling = c("all", "overdispersed", "weighted", "weighted_sq"),
known_sizes = NULL,
known_ind = NULL,
Correlation = NULL,
G1_ind = NULL,
G2_ind = NULL,
B2_ind = NULL,
N = NULL
)
Arguments
log_degrees |
The matrix of estimated raw log degrees from either the overdispersed or correlated models. |
log_prevalences |
The matrix of estimates raw log prevalences from either the overdispersed or correlated models. |
scaling |
An character vector providing the name of scaling procedure should be performed in order to transform estimates to degrees and subpopulation sizes. Scaling options are 'overdispersed', 'all' (the default), 'weighted', or 'weighted_sq' ('weighted' and 'weighted_sq' are only available if 'Correlation' is provided. Further details are provided in the Details section. |
known_sizes |
The known subpopulation sizes corresponding to a subset of
the columns of |
known_ind |
The indices that correspond to the columns of |
Correlation |
The estimated correlation matrix used to calculate scaling weights. Required if 'scaling = weighted' or 'scaling = weighted_sq'. |
G1_ind |
If 'scaling = overdispersed', a vector of indices corresponding to the subpopulations that belong to the primary scaling groups, i.e. the collection of rare girls' names in Zheng, Salganik, and Gelman (2006). By default, all known_sizes are used. If G2_ind and B2_ind are not provided, 'C = C_1', so only G1_ind are used. If G1_ind is not provided, no scaling is performed. |
G2_ind |
If 'scaling = overdispersed', a vector of indices corresponding to the subpopulations that belong to the first secondary scaling groups, i.e. the collection of somewhat popular girls' names. |
B2_ind |
If 'scaling = overdispersed', a vector of indices corresponding to the subpopulations that belong to the second secondary scaling groups, i.e. the collection of somewhat popular boys' names. |
N |
The known total population size. |
Details
The 'scaling' options are described below:
- NULL
No scaling is performed
- overdispersed
The scaling procedure outlined in Zheng et al. (2006) is performed. In this case, at least 'Pg1_ind' must be provided. See overdispersedStan for more details.
- all
All subpopulations with known sizes are used to scale the parameters, using a modified scaling procedure that standardizes the sizes so each population is weighted equally. Additional details are provided in Laga et al. (2021).
- weighted
All subpopulations with known sizes are weighted according their correlation with the unknown subpopulation size. Additional details are provided in Laga et al. (2021)
- weighted_sq
Same as 'weighted', except the weights are squared, providing more relative weight to subpopulations with higher correlation.
Value
The named list containing the scaled log degree, degree, log prevalence, and size estimates
References
Zheng, T., Salganik, M. J., and Gelman, A. (2006). How many people do you know in prison, Journal of the American Statistical Association, 101:474, 409–423
Laga, I., Bao, L., and Niu, X (2021). A Correlated Network Scaleup Model: Finding the Connection Between Subpopulations
Tracy-Widom test for residual group correlation
Description
Tracy-Widom test for residual group correlation
Usage
tw_group_corr_test(model_fit, correction = c("none", "half"), plot = TRUE)
Arguments
model_fit |
fitted model object |
correction |
correction constant, either "none", "half" |
plot |
a logical, whether to return a ggplot density plot of TW with observed statistic |
Value
a list containing test statistic, p-value, and diagnostic plots