Package 'sspse'

Title:	Estimating Hidden Population Size using Respondent Driven Sampling Data
Description:	Estimate the size of a networked population based on respondent-driven sampling data. The package is part of the "RDS Analyst" suite of packages for the analysis of respondent-driven sampling data. See Handcock, Gile and Mar (2014) <doi:10.1214/14-EJS923>, Handcock, Gile and Mar (2015) <doi:10.1111/biom.12255>, Kim and Handcock (2021) <doi:10.1093/jssam/smz055>, and McLaughlin, et. al. (2023) <doi:10.1214/23-AOAS1807>.
Authors:	Mark S. Handcock [aut, cre, cph] , Krista J. Gile [aut, cph], Brian Kim [ctb], Katherine R. McLaughlin [ctb]
Maintainer:	Mark S. Handcock <[email protected]>
License:	GPL-3 + file LICENSE
Version:	1.1.0-2
Built:	2024-11-06 03:57:28 UTC
Source:	https://github.com/cran/sspse

Help Index

Prior distributions for the size of a hidden population
A Pair of Simulated RDS Data Sets with no seed dependency
Estimates each person's personal visibility based on their self-reported degree and the number of their (direct) recruits. It uses the time the person was recruited as a factor in determining the number of recruits they produce.
Plots the posterior predictive p-values for the reported network sizes
Plot Summary and Diagnostics for Population Size Estimation Model Fits
Warning message for posteriorsize fit failure
Compute the posterior predictive p-values for the reported network sizes
Estimating hidden population size using RDS data
Summarizing Population Size Estimation Model Fits
Summarizing Population Size Estimation Model Fits

Prior distributions for the size of a hidden population

Description

dsizeprior computes the prior distribution of the population size of a hidden population. The prior is intended to be used in Bayesian inference for the population size based on data collected by Respondent Driven Sampling, but can be used with any Bayesian method to estimate population size.

Usage

dsizeprior(
  n,
  type = c("beta", "nbinom", "pln", "flat", "continuous", "supplied"),
  mean.prior.size = NULL,
  sd.prior.size = NULL,
  mode.prior.sample.proportion = NULL,
  median.prior.sample.proportion = NULL,
  median.prior.size = NULL,
  mode.prior.size = NULL,
  quartiles.prior.size = NULL,
  effective.prior.df = 1,
  alpha = NULL,
  beta = NULL,
  maxN = NULL,
  log = FALSE,
  maxbeta = 120,
  maxNmax = 2e+05,
  supplied = list(maxN = maxN),
  verbose = TRUE
)
dsizeprior(
  n,
  type = c("beta", "nbinom", "pln", "flat", "continuous", "supplied"),
  mean.prior.size = NULL,
  sd.prior.size = NULL,
  mode.prior.sample.proportion = NULL,
  median.prior.sample.proportion = NULL,
  median.prior.size = NULL,
  mode.prior.size = NULL,
  quartiles.prior.size = NULL,
  effective.prior.df = 1,
  alpha = NULL,
  beta = NULL,
  maxN = NULL,
  log = FALSE,
  maxbeta = 120,
  maxNmax = 2e+05,
  supplied = list(maxN = maxN),
  verbose = TRUE
)

Arguments

`n`	count; the sample size.
`type`	character; the type of parametric distribution to use for the prior on population size. The options are `"beta"` (for a Beta-type prior on the sample proportion (i.e. $n/N$ ), `"nbinom"` (Negative-Binomial), `"pln"` (Poisson-log-normal), `"flat"` (uniform), `continuous` (the continuous version of the Beta-type prior on the sample proportion). The last option is `"supplied"` which enables a numeric prior to be specified. See the argument `supplied` for the format of the information. The default `type` is `beta`.
`mean.prior.size`	scalar; A hyperparameter being the mean of the prior distribution on the population size.
`sd.prior.size`	scalar; A hyperparameter being the standard deviation of the prior distribution on the population size.
`mode.prior.sample.proportion`	scalar; A hyperparameter being the mode of the prior distribution on the sample proportion $n/N$ .
`median.prior.sample.proportion`	scalar; A hyperparameter being the median of the prior distribution on the sample proportion $n/N$ .
`median.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`mode.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`quartiles.prior.size`	vector of length 2; A pair of hyperparameters being the lower and upper quartiles of the prior distribution on the population size. For example, `quartiles.prior.size=c(1000,4000)` corresponds to a prior where the lower quartile (25%) is 1000 and the upper (75%) is 4000.
`effective.prior.df`	scalar; A hyperparameter being the effective number of samples worth of information represented in the prior distribution on the population size. By default this is 1, but it can be greater (or less!) to allow for different levels of uncertainty.
`alpha`	scalar; A hyperparameter being the first parameter of the Beta prior model for the sample proportion. By default this is NULL, meaning that 1 is chosen. it can be any value at least 1 to allow for different levels of uncertainty.
`beta`	scalar; A hyperparameter being the second parameter of the Beta prior model for the sample proportion. By default this is NULL, meaning that 1 is chosen. it can be any value at least 1 to allow for different levels of uncertainty.
`maxN`	integer; maximum possible population size. By default this is determined from an upper quantile of the prior distribution.
`log`	logical; return the prior or the the logarithm of the prior.
`maxbeta`	integer; maximum beta in the prior for population size. By default this is determined to ensure numerical stability.
`maxNmax`	integer; maximum possible population size. By default this is determined to ensure numerical stability.
`supplied`	list; If the argument `type="supplied"` then this should be a list object, typically of class `sspse`. It is primarily used to pass the posterior sample from a separate `size` call for use as the prior to this call. Essentially, it must have two components named `maxN` and `sample`. `maxN` is the maximum population envisaged and `sample` is random sample from the prior distribution.
`verbose`	logical; if this is `TRUE`, the program will print out additional information, including goodness of fit statistics.

Value

dsizeprior returns a list consisting of the following elements:

`x`	vector; vector of degrees `1:N` at which the prior PMF is computed.
`lpriorm`	vector; vector of probabilities corresponding to the values in `x`.
`N`	scalar; a starting value for the population size computed from the prior.
`maxN`	integer; maximum possible population size. By default this is determined from an upper quantile of the prior distribution.
`mean.prior.size`	scalar; A hyperparameter being the mean of the prior distribution on the population size.
`mode.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`effective.prior.df`	scalar; A hyperparameter being the effective number of samples worth of information represented in the prior distribution on the population size. By default this is 1, but it can be greater (or less!) to allow for different levels of uncertainty.
`mode.prior.sample.proportion`	scalar; A hyperparameter being the mode of the prior distribution on the sample proportion $n/N$ .
`median.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`beta`	scalar; A hyperparameter being the second parameter of the Beta distribution that is a component of the prior distribution on the sample proportion $n/N$ .
`type`	character; the type of parametric distribution to use for the prior on population size. The possible values are `beta` (for a Beta prior on the sample proportion (i.e. $n/N$ ), `nbinom` (Negative-Binomial), `pln` (Poisson-log-normal), `flat` (uniform), and `continuous` (the continuous version of the Beta prior on the sample proportion. The default is `beta`.

Details on priors

References

Gile, Krista J. (2008) Inference from Partially-Observed Network Data, Ph.D. Thesis, Department of Statistics, University of Washington.

Gile, Krista J. and Handcock, Mark S. (2010) Respondent-Driven Sampling: An Assessment of Current Methodology, Sociological Methodology 40, 285-327.

Gile, Krista J. and Handcock, Mark S. (2014) sspse: Estimating Hidden Population Size using Respondent Driven Sampling Data R package, Los Angeles, CA. Version 0.5, https://hpmrg.org/sspse/.

Handcock MS (2003). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.2, https://statnet.org/.

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2014) Estimating Hidden Population Size using Respondent-Driven Sampling Data, Electronic Journal of Statistics, 8, 1, 1491-1521

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2015) Estimating the Size of Populations at High Risk for HIV using Respondent-Driven Sampling Data, Biometrics.

Examples


prior <- dsizeprior(n=100,
                    type="beta",
                    mode.prior.size=1000)

prior <- dsizeprior(n=100,
                    type="beta",
                    mode.prior.size=1000)

A Pair of Simulated RDS Data Sets with no seed dependency

Description

This is a faux set used to illustrate how the estimators for multiple Respondent-Driven sampling surveys perform under different populations and RDS schemes.

Format

A list with the first element being an rds.data.frame of the first survey and the second element being an rds.data.frame of the second survey.

Details

The population is based on fauxmadrona from the RDS package. It is a population with N=1000 nodes from which two successive respondent-driven samples are drawn. For the first survey, the sample size is 200 so that there is a relatively small sample fraction (20%). There is homophily on disease status (R=5) and there is differential activity by disease status whereby the infected nodes have mean degree twice that of the uninfected (w=1.8).

In the sampling, the seeds are chosen randomly from the full population, so there is no dependency induced by seed selection.

Each sample member is given 2 uniquely identified coupons to distribute to other members of the target population in their acquaintance. Further each respondent distributes their coupons completely at random from among those they are connected to.

For the second sample the sample size is 250. The second survey has an additional variable recapture indicating if the respondent was also surveyed in the first survey.

Each survey is represented as an rds.data.frame and they are stored in a list with two elements.

Source

The original network is included in the RDS package as fauxmadrona.network, a network object.
The RDS package also includes a third respondent-driven sample from the network and is referred to as fauxmadrona.
Use data(package="sspse") to get a full list of datasets.

References

Gile, Krista J., Handcock, Mark S., 2010 Respondent-driven Sampling: An Assessment of Current Methodology, Sociological Methodology, 40, 285-327. doi:10.1111/j.1467-9531.2010.01223.x.

Kim, Brian J. and Handcock, Mark S. 2021 Population Size Estimation Using Multiple Respondent-Driven Sampling Surveys, Journal of Survey Statistics and Methodology, 9(1):94–120. doi:10.1093/jssam/smz055.

Estimates each person's personal visibility based on their self-reported degree and the number of their (direct) recruits. It uses the time the person was recruited as a factor in determining the number of recruits they produce.

Description

Estimates each person's personal visibility based on their self-reported degree and the number of their (direct) recruits. It uses the time the person was recruited as a factor in determining the number of recruits they produce.

Usage

impute.visibility(
  rds.data,
  max.coupons = NULL,
  type.impute = c("median", "distribution", "mode", "mean"),
  recruit.time = NULL,
  include.tree = FALSE,
  reflect.time = FALSE,
  parallel = 1,
  parallel.type = "PSOCK",
  interval = 10,
  burnin = 5000,
  mem.optimism.prior = NULL,
  df.mem.optimism.prior = 5,
  mem.scale.prior = 2,
  df.mem.scale.prior = 10,
  mem.overdispersion = 15,
  return.posterior.sample.visibilities = FALSE,
  verbose = FALSE
)
impute.visibility(
  rds.data,
  max.coupons = NULL,
  type.impute = c("median", "distribution", "mode", "mean"),
  recruit.time = NULL,
  include.tree = FALSE,
  reflect.time = FALSE,
  parallel = 1,
  parallel.type = "PSOCK",
  interval = 10,
  burnin = 5000,
  mem.optimism.prior = NULL,
  df.mem.optimism.prior = 5,
  mem.scale.prior = 2,
  df.mem.scale.prior = 10,
  mem.overdispersion = 15,
  return.posterior.sample.visibilities = FALSE,
  verbose = FALSE
)

Arguments

`rds.data`	An rds.data.frame
`max.coupons`	The number of recruitment coupons distributed to each enrolled subject (i.e. the maximum number of recruitees for any subject). By default it is taken by the attribute or data, else the maximum recorded number of coupons.
`type.impute`	The type of imputation based on the conditional distribution. It can be of type `distribution`,`mode`,`median`, or `mean` with the first , the default, being a random draw from the conditional distribution.
`recruit.time`	vector; An optional value for the data/time that the person was interviewed. It needs to resolve as a numeric vector with number of elements the number of rows of the data with non-missing values of the network variable. If it is a character name of a variable in the data then that variable is used. If it is NULL then the sequence number of the recruit in the data is used. If it is NA then the recruitment is not used in the model. Otherwise, the recruitment time is used in the model to better predict the visibility of the person.
`include.tree`	logical; If `TRUE`, augment the reported network size by the number of recruits and one for the recruiter (if any). This reflects a more accurate value for the visibility, but is not the self-reported degree. In particular, it typically produces a positive visibility (compared to a possibility zero self-reported degree).
`reflect.time`	logical; If `FALSE` then the `recruit.time` is the time before the end of the study (instead of the time since the survey started or chronological time).
`parallel`	count; the number of parallel processes to run for the Monte-Carlo sample. This uses MPI or PSOCK. The default is 1, that is not to use parallel processing.
`parallel.type`	The type of parallel processing to use. The options are "PSOCK" or "MPI". This requires the corresponding type to be installed. The default is "PSOCK".
`interval`	count; the number of proposals between sampled statistics.
`burnin`	count; the number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
`mem.optimism.prior`	scalar; A hyper parameter being the mean of the distribution of the optimism parameter.
`df.mem.optimism.prior`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the optimism parameter. This gives the equivalent sample size that would contain the same amount of information inherent in the prior.
`mem.scale.prior`	scalar; A hyper parameter being the scale of the concentration of baseline negative binomial measurement error model.
`df.mem.scale.prior`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the standard deviation of the dispersion parameter in the visibility model. This gives the equivalent sample size that would contain the same amount of information inherent in the prior for the standard deviation.
`mem.overdispersion`	scalar; A parameter being the overdispersion of the negative binomial distribution that is the baseline for the measurement error model.
`return.posterior.sample.visibilities`	logical; If TRUE then return a matrix of dimension `samplesize` by `n` of posterior draws from the visibility distribution for those in the survey. The sample for the `i`th person is the `i`th column. The default is FALSE so that the vector of imputes defined by `type.impute` is returned.
`verbose`	logical; if this is `TRUE`, the program will print out additional

References

McLaughlin, Katherine R.; Johnston, Lisa G.; Jakupi, Xhevat; Gexha-Bunjaku, Dafina; Deva, Edona and Handcock, Mark S. (2023) Modeling the Visibility Distribution for Respondent-Driven Sampling with Application to Population Size Estimation, Annals of Applied Statistics, doi:10.1093/jrsssa/qnad031

Examples

## Not run: 
data(fauxmadrona)
# The next line fits the model for the self-reported personal
# network sizes and imputes the personal network sizes 
# It may take up to 60 seconds.
visibility <- impute.visibility(fauxmadrona)
# frequency of estimated personal visibility
table(visibility)

## End(Not run)
## Not run: 
data(fauxmadrona)
# The next line fits the model for the self-reported personal
# network sizes and imputes the personal network sizes 
# It may take up to 60 seconds.
visibility <- impute.visibility(fauxmadrona)
# frequency of estimated personal visibility
table(visibility)

## End(Not run)

Plots the posterior predictive p-values for the reported network sizes

Description

This function extracts from an estimate of the posterior distribution of the population size based on data collected by Respondent Driven Sampling. The approach approximates the RDS via the Sequential Sampling model of Gile (2008). As such, it is referred to as the Sequential Sampling - Population Size Estimate (SS-PSE). It uses the order of selection of the sample to provide information on the distribution of network sizes over the population members.

Usage

## S3 method for class 'pospreddeg'
plot(
  x,
  main = "Posterior Predictive p-values for the self-reported network sizes",
  nclass = 20,
  hist = FALSE,
  ylim = c(0, 2),
  order.by.recruitment.time = FALSE,
  ...
)
## S3 method for class 'pospreddeg'
plot(
  x,
  main = "Posterior Predictive p-values for the self-reported network sizes",
  nclass = 20,
  hist = FALSE,
  ylim = c(0, 2),
  order.by.recruitment.time = FALSE,
  ...
)

Arguments

`x`	an object of class `"pospreddeg"`, usually, a result of a call to `pospreddeg`.
`main`	character; title for the plot
`nclass`	count; The number of classes for the histogram plot
`hist`	logical; If `TRUE` plot a histogram of the p-values rather than a density estimate.
`ylim`	two-vector; lower and upper limits of vertical/density axis.
`order.by.recruitment.time`	logical; If `TRUE`, the reorder the input data by the recruitment time
`...`	further arguments passed to or from other methods.

Details

It computes the posterior predictive distribution for each reported network size and computes the percentile rank of the reported network size within that posterior. The percentile rank should be about 0.5 for a well specified model, but could be close to uniform if there is little information about the reported network size. The percentile ranks should not be extreme (e.g., close to zero or one) on a consistent basis as this indicates a misspecified model.

References

Gile, Krista J. (2008) Inference from Partially-Observed Network Data, Ph.D. Thesis, Department of Statistics, University of Washington.

Gile, Krista J. and Handcock, Mark S. (2010) Respondent-Driven Sampling: An Assessment of Current Methodology, Sociological Methodology 40, 285-327.

Gile, Krista J. and Handcock, Mark S. (2014) sspse: Estimating Hidden Population Size using Respondent Driven Sampling Data R package, Los Angeles, CA. Version 0.5, https://hpmrg.org/sspse/.

Handcock MS (2003). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.2, https://statnet.org/.

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2014) Estimating Hidden Population Size using Respondent-Driven Sampling Data, Electronic Journal of Statistics, 8, 1, 1491-1521

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2015) Estimating the Size of Populations at High Risk for HIV using Respondent-Driven Sampling Data, Biometrics.

Examples


## Not run: 
data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=10, interval=1, samplesize=50)
summary(fit)
# Let's look at some MCMC diagnostics
plot(pospreddeg(fit))

## End(Not run)

## Not run: 
data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=10, interval=1, samplesize=50)
summary(fit)
# Let's look at some MCMC diagnostics
plot(pospreddeg(fit))

## End(Not run)

Plot Summary and Diagnostics for Population Size Estimation Model Fits

Description

This is the plot method for class "sspse". Objects of this class encapsulate the estimate of the posterior distribution of the population size based on data collected by Respondent Driven Sampling. The approach approximates the RDS via the Sequential Sampling model of Gile (2008). As such, it is referred to as the Sequential Sampling - Population Size Estimate (SS-PSE). It uses the order of selection of the sample to provide information on the distribution of network sizes over the population members.

Usage

## S3 method for class 'sspse'
plot(
  x,
  xlim = NULL,
  support = 1000,
  HPD.level = 0.9,
  N = NULL,
  ylim = NULL,
  mcmc = FALSE,
  type = "all",
  main = "Posterior for population size",
  smooth = 4,
  include.tree = TRUE,
  cex.main = 1,
  log.degree = "",
  method = "bgk",
  ...
)
## S3 method for class 'sspse'
plot(
  x,
  xlim = NULL,
  support = 1000,
  HPD.level = 0.9,
  N = NULL,
  ylim = NULL,
  mcmc = FALSE,
  type = "all",
  main = "Posterior for population size",
  smooth = 4,
  include.tree = TRUE,
  cex.main = 1,
  log.degree = "",
  method = "bgk",
  ...
)

Arguments

`x`	an object of class `"plot.sspse"`, usually, a result of a call to `plot.sspse`.
`xlim`	the (optional) x limits (x1, x2) of the plot of the posterior of the population size.
`support`	the number of equally-spaced points to use for the support of the estimated posterior density function.
`HPD.level`	numeric; probability level of the highest probability density interval determined from the estimated posterior.
`N`	Optionally, an estimate of the population size to mark on the plots as a reference point.
`ylim`	the (optional) vertical limits (y1, y2) of the plot of the posterior of the population size. A vertical axis is the probability density scale.
`mcmc`	logical; If TRUE, additionally create simple diagnostic plots for the MCMC sampled statistics produced from the fit.
`type`	character; This controls the types of plots produced. If `"N"`, a density plot of the posterior for population size is produced. and the prior for population size is overlaid. If `"summary"`, a density plot of the posterior for mean visibility in the population and a plot of the posterior for standard deviation of the visibility in the population. If `"visibility"`, a density plot of the visibility distribution (its posterior mean) and the same plot with the with visibilities of those in the sample overlaid. If `"degree"`, a scatter plot of the visibilities verses the reported network sizes for those in the sample. If `"prior"`, a density plot of the prior for population size is produced. If `"all"`, then all plots for `"N"`, `"summary"`, `"visibility"` and `"degree"` are produced. In all cases the visibilities are estimated (by their posterior means).
`main`	an overall title for the posterior plot.
`smooth`	the (optional) smoothing parameter for the density estimate.
`include.tree`	logical; If `TRUE`, augment the reported network size by the number of recruits and one for the recruiter (if any). This reflects a more accurate value for the visibility, but is not the reported degree. In particular, it typically produces a positive visibility (compared to a possibility zero reported degree).
`cex.main`	an overall title for the posterior plot.
`log.degree`	a character string which contains `"x"` if the (horizontal) degree axis in the plot of the estimated visibilites for each respondent verses their reported network sizes be logarithmic. A value of `"y"` uses a logarithmic visibility axis and `"xy"` both. The default is `""`, no logarithmic axes.
`method`	character; The method to use for density estimation (default Gaussian Kernel; "bgk"). "Bayes" uses a Bayesian density estimator which has good properties.
`...`	further arguments passed to or from other methods.

Details

By default it produces a density plot of the posterior for population size and the prior for population size is overlaid. It also produces a density plot of the posterior for mean network size in the population, the posterior for standard deviation of the network size, and a density plot of the posterior mean network size distribution with sample histogram overlaid.

References

Gile, Krista J. (2008) Inference from Partially-Observed Network Data, Ph.D. Thesis, Department of Statistics, University of Washington.

Gile, Krista J. and Handcock, Mark S. (2010) Respondent-Driven Sampling: An Assessment of Current Methodology, Sociological Methodology 40, 285-327.

Gile, Krista J. and Handcock, Mark S. (2014) sspse: Estimating Hidden Population Size using Respondent Driven Sampling Data R package, Los Angeles, CA. Version 0.5, https://hpmrg.org.

Handcock MS (2003). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.2, https://statnet.org.

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2014) Estimating Hidden Population Size using Respondent-Driven Sampling Data, Electronic Journal of Statistics, 8, 1, 1491-1521

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2015) Estimating the Size of Populations at High Risk for HIV using Respondent-Driven Sampling Data, Biometrics.

Examples


## Not run: 
data(fauxmadrona)
# Here interval=1 and samplesize=50 so that it will run faster. It should be much higher
# in a real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                  burnin=10, interval=1, samplesize=50)
summary(fit)
# Let's look at some MCMC diagnostics
plot(fit, mcmc=TRUE)

## End(Not run)

## Not run: 
data(fauxmadrona)
# Here interval=1 and samplesize=50 so that it will run faster. It should be much higher
# in a real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                  burnin=10, interval=1, samplesize=50)
summary(fit)
# Let's look at some MCMC diagnostics
plot(fit, mcmc=TRUE)

## End(Not run)

Warning message for posteriorsize fit failure

Description

posteriorsize computes the posterior distribution of the population size based on data collected by Respondent Driven Sampling. This function returns the warning message if it fails. It enables packages that call posteriorsize to use a consistent error message.

Usage

posize_warning()
posize_warning()

Value

posize_warning returns a character string witn the warning message.

Compute the posterior predictive p-values for the reported network sizes

Description

Usage

pospreddeg(x, order.by.recruitment.time = FALSE)
pospreddeg(x, order.by.recruitment.time = FALSE)

Arguments

`x`	an object of class `"sspse"`, usually, a result of a call to `oosteriorsize`.
`order.by.recruitment.time`	logical; If `TRUE`, the reorder the input data by the recruitment time

Details

References

Gile, Krista J. (2008) Inference from Partially-Observed Network Data, Ph.D. Thesis, Department of Statistics, University of Washington.

Gile, Krista J. and Handcock, Mark S. (2010) Respondent-Driven Sampling: An Assessment of Current Methodology, Sociological Methodology 40, 285-327.

Gile, Krista J. and Handcock, Mark S. (2014) sspse: Estimating Hidden Population Size using Respondent Driven Sampling Data R package, Los Angeles, CA. Version 0.5, https://hpmrg.org/sspse/.

Handcock MS (2003). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.2, https://statnet.org/.

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2014) Estimating Hidden Population Size using Respondent-Driven Sampling Data, Electronic Journal of Statistics, 8, 1, 1491-1521

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2015) Estimating the Size of Populations at High Risk for HIV using Respondent-Driven Sampling Data, Biometrics.

Examples


## Not run: 
data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
summary(fit)
# Let's look at some MCMC diagnostics
pospreddeg(fit)

## End(Not run)

## Not run: 
data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
summary(fit)
# Let's look at some MCMC diagnostics
pospreddeg(fit)

## End(Not run)

Estimating hidden population size using RDS data

Description

posteriorsize computes the posterior distribution of the population size based on data collected by Respondent Driven Sampling. The approach approximates the RDS via the Sequential Sampling model of Gile (2008). As such, it is referred to as the Sequential Sampling - Population Size Estimate (SS-PSE). It uses the order of selection of the sample to provide information on the distribution of network sizes over the population members.

Usage

posteriorsize(
  s,
  s2 = NULL,
  previous = NULL,
  median.prior.size = NULL,
  interval = 10,
  burnin = 5000,
  maxN = NULL,
  K = FALSE,
  samplesize = 1000,
  quartiles.prior.size = NULL,
  mean.prior.size = NULL,
  mode.prior.size = NULL,
  priorsizedistribution = c("beta", "flat", "nbinom", "pln", "supplied"),
  effective.prior.df = 1,
  sd.prior.size = NULL,
  mode.prior.sample.proportion = NULL,
  alpha = NULL,
  visibilitydistribution = c("cmp", "nbinom", "pln"),
  mean.prior.visibility = NULL,
  sd.prior.visibility = NULL,
  max.sd.prior.visibility = 4,
  df.mean.prior.visibility = 1,
  df.sd.prior.visibility = 3,
  beta_0.mean.prior = -3,
  beta_t.mean.prior = 0,
  beta_u.mean.prior = 0,
  beta_0.sd.prior = 10,
  beta_t.sd.prior = 10,
  beta_u.sd.prior = 10,
  mem.optimism.prior = NULL,
  df.mem.optimism.prior = 5,
  mem.scale.prior = 2,
  df.mem.scale.prior = 10,
  mem.overdispersion = 15,
  visibility = TRUE,
  type.impute = c("median", "distribution", "mode", "mean"),
  Np = 0,
  n = NULL,
  n2 = NULL,
  mu_proposal = 0.1,
  nu_proposal = 0.15,
  beta_0_proposal = 0.2,
  beta_t_proposal = 0.001,
  beta_u_proposal = 0.001,
  memmu_proposal = 0.1,
  memscale_proposal = 0.15,
  burnintheta = 500,
  burninbeta = 50,
  parallel = 1,
  parallel.type = "PSOCK",
  seed = NULL,
  maxbeta = 90,
  supplied = list(maxN = maxN),
  max.coupons = NULL,
  recruit.time = NULL,
  recruit.time2 = NULL,
  include.tree = TRUE,
  unit.scale = FALSE,
  optimism = TRUE,
  reflect.time = FALSE,
  equalize = TRUE,
  verbose = FALSE
)
posteriorsize(
  s,
  s2 = NULL,
  previous = NULL,
  median.prior.size = NULL,
  interval = 10,
  burnin = 5000,
  maxN = NULL,
  K = FALSE,
  samplesize = 1000,
  quartiles.prior.size = NULL,
  mean.prior.size = NULL,
  mode.prior.size = NULL,
  priorsizedistribution = c("beta", "flat", "nbinom", "pln", "supplied"),
  effective.prior.df = 1,
  sd.prior.size = NULL,
  mode.prior.sample.proportion = NULL,
  alpha = NULL,
  visibilitydistribution = c("cmp", "nbinom", "pln"),
  mean.prior.visibility = NULL,
  sd.prior.visibility = NULL,
  max.sd.prior.visibility = 4,
  df.mean.prior.visibility = 1,
  df.sd.prior.visibility = 3,
  beta_0.mean.prior = -3,
  beta_t.mean.prior = 0,
  beta_u.mean.prior = 0,
  beta_0.sd.prior = 10,
  beta_t.sd.prior = 10,
  beta_u.sd.prior = 10,
  mem.optimism.prior = NULL,
  df.mem.optimism.prior = 5,
  mem.scale.prior = 2,
  df.mem.scale.prior = 10,
  mem.overdispersion = 15,
  visibility = TRUE,
  type.impute = c("median", "distribution", "mode", "mean"),
  Np = 0,
  n = NULL,
  n2 = NULL,
  mu_proposal = 0.1,
  nu_proposal = 0.15,
  beta_0_proposal = 0.2,
  beta_t_proposal = 0.001,
  beta_u_proposal = 0.001,
  memmu_proposal = 0.1,
  memscale_proposal = 0.15,
  burnintheta = 500,
  burninbeta = 50,
  parallel = 1,
  parallel.type = "PSOCK",
  seed = NULL,
  maxbeta = 90,
  supplied = list(maxN = maxN),
  max.coupons = NULL,
  recruit.time = NULL,
  recruit.time2 = NULL,
  include.tree = TRUE,
  unit.scale = FALSE,
  optimism = TRUE,
  reflect.time = FALSE,
  equalize = TRUE,
  verbose = FALSE
)

Arguments

`s`	either a vector of integers or an `rds.data.frame` providing network size information. If a `rds.data.frame` is passed and `visibility=TRUE`, the default, then the measurement error model is to used, whereby latent visibilities are used in place of the reported network sizes as the size variable. If a vector of integers is passed these are the network sizes in sequential order of recording (and the measurement model is not used).
`s2`	either a vector of integers or an `rds.data.frame` providing network size information for a second RDS sample subsequent to the first RDS recorded in $s$ . If a `rds.data.frame` is passed and `visibility=TRUE`, the default, then the measurement error model is to used, whereby latent visibilities are used in place of the reported network sizes as the size variable. If a vector of integers is passed these are the network sizes in sequential order of recording (and the measurement model is not used).
`previous`	character; optionally, the name of the variable in $s2$ indicating if the corresponding unit was sampled in the first RDS.
`median.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`interval`	count; the number of proposals between sampled statistics.
`burnin`	count; the number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
`maxN`	integer; maximum possible population size. By default this is determined from an upper quantile of the prior distribution.
`K`	count; the maximum visibility for an individual. This is usually calculated as `round(stats::quantile(s,0.80))`. It applies to network sizes and (latent) visibilities. If logical and FALSE then the K is unbounded but set to compute the visibilities.
`samplesize`	count; the number of Monte-Carlo samples to draw to compute the posterior. This is the number returned by the Metropolis-Hastings algorithm.The default is 1000.
`quartiles.prior.size`	vector of length 2; A pair of hyperparameters being the lower and upper quartiles of the prior distribution on the population size. For example, `quartiles.prior.size=c(1000,4000)` corresponds to a prior where the lower quartile (25%) is 1000 and the upper (75%) is 4000.
`mean.prior.size`	scalar; A hyperparameter being the mean of the prior distribution on the population size.
`mode.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`priorsizedistribution`	character; the type of parametric distribution to use for the prior on population size. The options are `beta` (for a Beta prior on the sample proportion (i.e. $n/N$ )), `flat` (uniform), `nbinom` (Negative-Binomial), and `pln` (Poisson-log-normal). The default is `beta`.
`effective.prior.df`	scalar; A hyperparameter being the effective number of samples worth of information represented in the prior distribution on the population size. By default this is 1, but it can be greater (or less!) to allow for different levels of uncertainty.
`sd.prior.size`	scalar; A hyperparameter being the standard deviation of the prior distribution on the population size.
`mode.prior.sample.proportion`	scalar; A hyperparameter being the mode of the prior distribution on the sample proportion $n/N$ .
`alpha`	scalar; A hyperparameter being the first parameter of the beta prior model for the sample proportion. By default this is NULL, meaning that 1 is chosen. it can be any value at least 1 to allow for different levels of uncertainty.
`visibilitydistribution`	count; the parametric distribution to use for the individual network sizes (i.e., degrees). The options are `cmp`, `nbinom`, and `pln`. These correspond to the Conway-Maxwell-Poisson, Negative-Binomial, and Poisson-log-normal. The default is `cmp`.
`mean.prior.visibility`	scalar; A hyper parameter being the mean visibility for the prior distribution for a randomly chosen person. The prior has this mean.
`sd.prior.visibility`	scalar; A hyper parameter being the standard deviation of the visibility for a randomly chosen person. The prior has this standard deviation.
`max.sd.prior.visibility`	scalar; The maximum allowed value of `sd.prior.visibility`. If the passed or computed value is higher, it is reduced to this value. This is done for numerical stability reasons.
`df.mean.prior.visibility`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the mean. This gives the equivalent sample size that would contain the same amount of information inherent in the prior.
`df.sd.prior.visibility`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the standard deviation. This gives the equivalent sample size that would contain the same amount of information inherent in the prior for the standard deviation.
`beta_0.mean.prior`	scalar; A hyper parameter being the mean of the beta_0 parameter distribution in the model for the number of recruits.
`beta_t.mean.prior`	scalar; A hyper parameter being the mean of the beta_t parameter distribution in the model for the number of recruits. This corresponds to the time-to-recruit variable.
`beta_u.mean.prior`	scalar; A hyper parameter being the mean of the beta_u parameter distribution in the model for the number of recruits. This corresponds to the visibility variable.
`beta_0.sd.prior`	scalar; A hyper parameter being the standard deviation of the beta_0 parameter distribution in the model for the number of recruits.
`beta_t.sd.prior`	scalar; A hyper parameter being the standard deviation of the beta_t parameter distribution in the model for the number of recruits. This corresponds to the time-to-recruit variable.
`beta_u.sd.prior`	scalar; A hyper parameter being the standard deviation of the beta_u parameter distribution in the model for the number of recruits. This corresponds to the visibility variable.
`mem.optimism.prior`	scalar; A hyper parameter being the mean of the distribution of the optimism parameter.
`df.mem.optimism.prior`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the optimism parameter. This gives the equivalent sample size that would contain the same amount of information inherent in the prior.
`mem.scale.prior`	scalar; A hyper parameter being the scale of the concentration of baseline negative binomial measurement error model.
`df.mem.scale.prior`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the standard deviation of the dispersion parameter in the visibility model. This gives the equivalent sample size that would contain the same amount of information inherent in the prior for the standard deviation.
`mem.overdispersion`	scalar; A parameter being the overdispersion of the negative binomial distribution that is the baseline for the measurement error model.
`visibility`	logical; Indicate if the measurement error model is to be used, whereby latent visibilities are used in place of the reported network sizes as the unit size variable. If `TRUE` then a `rds.data.frame` need to be passed to provide the RDS information needed for the measurement error model.
`type.impute`	The type of imputation to use for the summary visibilities (returned in the component `visibilities`. The imputes are based on the posterior draws of the visibilities. It can be of type `distribution`, `mode`,`median`, or `mean` with `median` the default, being the posterior median of the visibility for that person.
`Np`	integer; The overall visibility distribution is a mixture of the `Np` rates for `1:Np` and a parametric visibility distribution model truncated below `Np`. Thus the model fits the proportions of the population with visibility `1:Np` each with a separate parameter. This should adjust for an lack-of-fit of the parametric visibility distribution model at lower visibilities, although it also changes the model away from the parametric visibility distribution model.
`n`	integer; the number of people in the sample. This is usually computed from $s$ automatically and not usually specified by the user.
`n2`	integer; If $s2$ is specified, this is the number of people in the second sample. This is usually computed from $s$ automatically and not usually specified by the user.
`mu_proposal`	scalar; The standard deviation of the proposal distribution for the mean visibility.
`nu_proposal`	scalar; The standard deviation of the proposal distribution for the CMP scale parameter that determines the standard deviation of the visibility.
`beta_0_proposal`	scalar; The standard deviation of the proposal distribution for the beta_0 parameter of the recruit model.
`beta_t_proposal`	scalar; The standard deviation of the proposal distribution for the beta_t parameter of the recruit model. This corresponds to the visibility variable.
`beta_u_proposal`	scalar; The standard deviation of the proposal distribution for the beta_u parameter of the recruit model. This corresponds to the time-to-recruit variable.
`memmu_proposal`	scalar; The standard deviation of the proposal distribution for the log of the optimism parameter (that is, gamma).
`memscale_proposal`	scalar; The standard deviation of the proposal distribution for the log of the s.d. in the optimism model.
`burnintheta`	count; the number of proposals in the Metropolis-Hastings sub-step for the visibility distribution parameters ( $\theta$ ) before any MCMC sampling is done. It typically is set to a modestly large number.
`burninbeta`	count; the number of proposals in the Metropolis-Hastings sub-step for the visibility distribution parameters ( $\beta$ ) before any MCMC sampling is done. It typically is set to a modestly large number.
`parallel`	count; the number of parallel processes to run for the Monte-Carlo sample. This uses MPI or PSOCK. The default is 1, that is not to use parallel processing.
`parallel.type`	The type of parallel processing to use. The options are "PSOCK" or "MPI". This requires the corresponding type to be installed. The default is "PSOCK".
`seed`	integer; random number integer seed. Defaults to `NULL` to use whatever the state of the random number generator is at the time of the call.
`maxbeta`	scalar; The maximum allowed value of the `beta` parameter. If the implied or computed value is higher, it is reduced to this value. This is done for numerical stability reasons.
`supplied`	list; If supplied, is a list with components `maxN` and `sample`. In this case `supplied` is a matrix with a column named `N` being a sample from a prior distribution for the population size. The value `maxN` specifies the maximum value of the population size, a priori.
`max.coupons`	The number of recruitment coupons distributed to each enrolled subject (i.e. the maximum number of recruitees for any subject). By default it is taken by the attribute or data, else the maximum recorded number of coupons.
`recruit.time`	vector; An optional value for the data/time that the person was interviewed. It needs to resolve as a numeric vector with number of elements the number of rows of the data with non-missing values of the network variable. If it is a character name of a variable in the data then that variable is used. If it is NULL then the sequence number of the recruit in the data is used. If it is NA then the recruitment is not used in the model. Otherwise, the recruitment time is used in the model to better predict the visibility of the person.
`recruit.time2`	vector; An optional value for the data/time that the person in the second RDS survey was interviewed. It needs to resolve as a numeric vector with number of elements the number of rows of the data with non-missing values of the network variable. If it is a character name of a variable in the data then that variable is used. If it is NULL, the default, then the sequence number of the recruit in the data is used. If it is NA then the recruitment is not used in the model. Otherwise, the recruitment time is used in the model to better predict the visibility of the person.
`include.tree`	logical; If `TRUE`, augment the reported network size by the number of recruits and one for the recruiter (if any). This reflects a more accurate value for the visibility, but is not the self-reported degree. In particular, it typically produces a positive visibility (compared to a possibility zero self-reported degree).
`unit.scale`	numeric; If not `NULL` it sets the numeric value of the scale parameter of the distribution of the unit sizes. For the negative binomial, it is the multiplier on the variance of the negative binomial compared to a Poisson (via the Poisson-Gamma mixture representation). Sometimes the scale is unnaturally large (e.g. 40) so this give the option of fixing it (rather than using the MLE of it). The model is fit with the parameter fixed at this passed value.
`optimism`	logical; If `TRUE` then add a term to the model allowing the (proportional) inflation of the self-reported degrees relative to the unit sizes.
`reflect.time`	logical; If `TRUE` then the `recruit.time` is the time before the end of the study (instead of the time since the survey started or chronological time).
`equalize`	logical; If `TRUE` and the capture-recapture model is used, adjusts for gross differences in the reported network sizes between the two samples.
`verbose`	logical; if this is `TRUE`, the program will print out additional information, including goodness of fit statistics.

Value

posteriorsize returns a list consisting of the following elements:

`pop`	vector; The final posterior draw for the degrees of the population. The first $n$ are the sample in sequence and the reminder are non-sequenced.
`K`	count; the maximum visibility for an individual. This is usually calculated as twice the maximum observed degree.
`n`	count; the sample size.
`samplesize`	count; the number of Monte-Carlo samples to draw to compute the posterior. This is the number returned by the Metropolis-Hastings algorithm.The default is 1000.
`burnin`	count; the number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
`interval`	count; the number of proposals between sampled statistics.
`mu`	scalar; The hyper parameter `mean.prior.visibility` being the mean visibility for the prior distribution for a randomly chosen person. The prior has this mean.
`sigma`	scalar; The hyper parameter `sigma` being the standard deviation of the visibility for a randomly chosen person. The prior has this standard deviation.
`df.mean.prior.visibility`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the mean. This gives the equivalent sample size that would contain the same amount of information inherent in the prior.
`df.sd.prior.visibility`	scalar; A hyper parameter being the degrees-of-freedom of the prior for the standard deviation. This gives the equivalent sample size that would contain the same amount of information inherent in the prior for the standard deviation.
`Np`	integer; The overall visibility distribution is a mixture of the `1:Np` rates and a parametric visibility distribution model truncated below Np. Thus the model fits the proportions of the population with visibility `1:Np` each with a separate parameter. This should adjust for an lack-of-fit of the parametric visibility distribution model at lower visibilities, although it also changes the model away from the parametric visibility distribution model.
`mu_proposal`	scalar; The standard deviation of the proposal distribution for the mean visibility.
`nu_proposal`	scalar; The standard deviation of the proposal distribution for the CMP scale parameter of the visibility distribution.
`N`	vector of length 5; summary statistics for the posterior population size. MAP maximum aposteriori value of N Mean AP mean aposteriori value of N Median AP median aposteriori value of N P025 the 2.5th percentile of the (posterior) distribution for the N. That is, the lower point on a 95% probability interval. P975 the 97.5th percentile of the (posterior) distribution for the N. That is, the upper point on a 95% probability interval.
`maxN`	integer; maximum possible population size. By default this is determined from an upper quantile of the prior distribution.
`sample`	matrix of dimension `samplesize` $\times$ `10` matrix of summary statistics from the posterior. This is also an object of class `mcmc` so it can be plotted and summarized via the `mcmc.diagnostics` function in the `ergm` package (and also the `coda` package). The statistics are: N population size. mu scalar; The mean visibility for the prior distribution for a randomly chosen person. The prior has this mean. sigma scalar; The standard deviation of the visibility for a randomly chosen person. The prior has this standard deviation. visibility1 scalar; the number of nodes of visibility 1 in the population (it is assumed all nodes have visibility 1 or more). lambda scalar; This is only present for the `cmp` model. It is the $\lambda$ parameter in the standard parameterization of the Conway-Maxwell-Poisson model for the visibility distribution. nu scalar; This is only present for the `cmp` model. It is the $\nu$ parameter in the standard parameterization of the Conway-Maxwell-Poisson model for the visibility distribution.
`vsample`	matrix of dimension `samplesize` $\times$ `n` matrix of posterior draws from the unit size distribution for those in the survey. The sample for the `i`th person is the `i`th column.
`lpriorm`	vector; the vector of (log) prior probabilities on each value of $m=N-n$ - that is, the number of unobserved members of the population. The values are `n:(length(lpriorm)-1+n)`.
`burnintheta`	count; the number of proposals in the Metropolis-Hastings sub-step for the visibility distribution parameters ( $\theta$ ) before any MCMC sampling is done. It typically is set to a modestly large number.
`verbose`	logical; if this is `TRUE`, the program printed out additional information, including goodness of fit statistics.
`predictive.visibility.count`	vector; a vector of length the maximum visibility (`K`) (by default `K=2*max(sample visibility)`). The `k`th entry is the posterior predictive number persons with visibility `k`. That is, it is the posterior predictive distribution of the number of people with each visibility in the population.
`predictive.visibility`	vector; a vector of length the maximum visibility (`K`) (by default `K=2*max(sample visibility)`). The `k`th entry is the posterior predictive proportion of persons with visibility `k`. That is, it is the posterior predictive distribution of the proportion of people with each visibility in the population.
`MAP`	vector of length 6 of MAP estimates corresponding to the output `sample`. These are: N population size. mu scalar; The mean visibility for the prior distribution for a randomly chosen person. The prior has this mean. sigma scalar; The standard deviation of the visibility for a randomly chosen person. The prior has this standard deviation. visibility1 scalar; the number of nodes of visibility 1 in the population (it is assumed all nodes have visibility 1 or more). lambda scalar; This is only present for the `cmp` model. It is the $\lambda$ parameter in the standard parameterization of the Conway-Maxwell-Poisson model for the visibility distribution. nu scalar; This is only present for the `cmp` model. It is the $\nu$ parameter in the standard parameterization of the Conway-Maxwell-Poisson model for the visibility distribution.
`mode.prior.sample.proportion`	scalar; A hyperparameter being the mode of the prior distribution on the sample proportion $n/N$ .
`median.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`mode.prior.size`	scalar; A hyperparameter being the mode of the prior distribution on the population size.
`mean.prior.size`	scalar; A hyperparameter being the mean of the prior distribution on the population size.
`quartiles.prior.size`	vector of length 2; A pair of hyperparameters being the lower and upper quartiles of the prior distribution on the population size.
`visibilitydistribution`	count; the parametric distribution to use for the individual network sizes (i.e., visibilities). The options are `cmp`, `nbinom`, and `pln`. These correspond to the Conway-Maxwell-Poisson, Negative-Binomial, and Poisson-log-normal. The default is `cmp`.
`priorsizedistribution`	character; the type of parametric distribution to use for the prior on population size. The options are `beta` (for a Beta prior on the sample proportion (i.e. $n/N$ ), `nbinom` (Negative-Binomial), `pln` (Poisson-log-normal), `flat` (uniform), and `continuous` (the continuous version of the Beta prior on the sample proportion. The default is `beta`.

Details on priors

The best way to specify the prior is via the hyperparameter mode.prior.size which specifies the mode of the prior distribution on the population size. You can alternatively specify the hyperparameter median.prior.size which specifies the median of the prior distribution on the population size, or mean.prior.sample proportion which specifies the mean of the prior distribution on the proportion of the population size in the sample or mode.prior.sample proportion which specifies the mode of the prior distribution on the proportion of the population size in the sample. Finally, you can specify quartiles.prior.size as a vector of length 2 being the pair of lower and upper quartiles of the prior distribution on the population size.

References

Gile, Krista J. (2008) Inference from Partially-Observed Network Data, Ph.D. Thesis, Department of Statistics, University of Washington.

Gile, Krista J. and Handcock, Mark S. (2010) Respondent-Driven Sampling: An Assessment of Current Methodology, Sociological Methodology 40, 285-327.

Gile, Krista J. and Handcock, Mark S. (2014) sspse: Estimating Hidden Population Size using Respondent Driven Sampling Data R package, Los Angeles, CA. Version 0.5, https://hpmrg.org/sspse/.

Handcock MS (2003). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.2, https://statnet.org/.

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2014) Estimating Hidden Population Size using Respondent-Driven Sampling Data, Electronic Journal of Statistics, 8, 1, 1491-1521

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2015) Estimating the Size of Populations at High Risk for HIV using Respondent-Driven Sampling Data, Biometrics.

Examples

data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
summary(fit)
data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
summary(fit)

Summarizing Population Size Estimation Model Fits

Description

This is the print method for the summary class method for class "sspse" objects. These objects encapsulate an estimate of the posterior distribution of the population size based on data collected by Respondent Driven Sampling. The approach approximates the RDS via the Sequential Sampling model of Gile (2008). As such, it is referred to as the Sequential Sampling - Population Size Estimate (SS-PSE). It uses the order of selection of the sample to provide information on the distribution of network sizes over the population members.

Usage

## S3 method for class 'summary.sspse'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  correlation = FALSE,
  covariance = FALSE,
  signif.stars = getOption("show.signif.stars"),
  eps.Pvalue = 1e-04,
  ...
)
## S3 method for class 'summary.sspse'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  correlation = FALSE,
  covariance = FALSE,
  signif.stars = getOption("show.signif.stars"),
  eps.Pvalue = 1e-04,
  ...
)

Arguments

`x`	an object of class `"summary.sspse"`, usually, a result of a call to `summary.sspse`.
`digits`	the number of significant digits to use when printing.
`correlation`	logical; if `TRUE`, the correlation matrix of the estimated parameters is returned and printed.
`covariance`	logical; if `TRUE`, the covariance matrix of the estimated parameters is returned and printed.
`signif.stars`	logical. If `TRUE`, ‘significance stars’ are printed for each coefficient.
`eps.Pvalue`	number; indicates the smallest p-value. `printCoefmat`.
`...`	further arguments passed to or from other methods.

Details

print.summary.sspse tries to be smart about formatting the coefficients, standard errors, etc. and additionally gives ‘significance stars’ if signif.stars is TRUE.

Aliased coefficients are omitted in the returned object but restored by the print method.

Correlations are printed to two decimal places (or symbolically): to see the actual correlations print summary(object)$correlation directly.

Value

The function summary.sspse computes and returns a two row matrix of summary statistics of the prior and estimated posterior distributions. The rows correspond to the Prior and the Posterior, respectively. The rows names are Mean, Median, Mode, 25%, 75%, and 90%. These correspond to the distributional mean, median, mode, lower quartile, upper quartile and 90% quantile, respectively.

References

Gile, Krista J. (2008) Inference from Partially-Observed Network Data, Ph.D. Thesis, Department of Statistics, University of Washington.

Gile, Krista J. and Handcock, Mark S. (2010) Respondent-Driven Sampling: An Assessment of Current Methodology, Sociological Methodology 40, 285-327.

Gile, Krista J. and Handcock, Mark S. (2014) sspse: Estimating Hidden Population Size using Respondent Driven Sampling Data R package, Los Angeles, CA. Version 0.5, https://hpmrg.org/sspse/.

Handcock MS (2003). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.2, https://statnet.org/.

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2014) Estimating Hidden Population Size using Respondent-Driven Sampling Data, Electronic Journal of Statistics, 8, 1, 1491-1521

Handcock, Mark S., Gile, Krista J. and Mar, Corinne M. (2015) Estimating the Size of Populations at High Risk for HIV using Respondent-Driven Sampling Data, Biometrics.

Examples


data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
fit

data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
fit

Summarizing Population Size Estimation Model Fits

Description

This is the summary method for class "sspse" objects. These objects encapsulate an estimate of the posterior distribution of the population size based on data collected by Respondent Driven Sampling. The approach approximates the RDS via the Sequential Sampling model of Gile (2008). As such, it is referred to as the Sequential Sampling - Population Size Estimate (SS-PSE). It uses the order of selection of the sample to provide information on the distribution of network sizes over the population members. summary method for class "sspse". posterior distribution of the population size based on data collected by Respondent Driven Sampling. The approach approximates the RDS via the Sequential Sampling model of Gile (2008). As such, it is referred to as the Sequential Sampling - Population Size Estimate (SS-PSE). It uses the order of selection of the sample to provide information on the distribution of network sizes over the population members.

Usage

## S3 method for class 'sspse'
summary(object, support = 1000, HPD.level = 0.95, method = "bgk", ...)
## S3 method for class 'sspse'
summary(object, support = 1000, HPD.level = 0.95, method = "bgk", ...)

Arguments

`object`	an object of class `"sspse"`, usually, a result of a call to `posteriorsize`.
`support`	the number of equally-spaced points to use for the support of the estimated posterior density function.
`HPD.level`	numeric; probability level of the highest probability density interval determined from the estimated posterior.
`method`	character; The method to use for density estimation (default Gaussian Kernel; "bgk"). "Bayes" uses a Bayesian density estimator which has good properties.
`...`	further arguments passed to or from other methods.

Details

print.summary.sspse tries to be smart about formatting the coefficients, standard errors, etc. and additionally gives ‘significance stars’ if signif.stars is TRUE.

Aliased coefficients are omitted in the returned object but restored by the print method.

Correlations are printed to two decimal places (or symbolically): to see the actual correlations print summary(object)$correlation directly.

Value

Examples


data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
summary(fit)

data(fauxmadrona)
# Here interval=1 so that it will run faster. It should be higher in a 
# real application.
fit <- posteriorsize(fauxmadrona, median.prior.size=1000,
                                 burnin=20, interval=1, samplesize=100)
summary(fit)

Package 'sspse'

Help Index

Prior distributions for the size of a hidden population

Description

Usage

Arguments

Value

Details on priors

References

See Also

Examples

A Pair of Simulated RDS Data Sets with no seed dependency

Description

Format

Details

Source

References

See Also

Estimates each person's personal visibility based on their self-reported degree and the number of their (direct) recruits. It uses the time the person was recruited as a factor in determining the number of recruits they produce.

Description

Usage

Arguments

References

Examples

Plots the posterior predictive p-values for the reported network sizes

Description

Usage

Arguments

Details

References

See Also

Examples

Plot Summary and Diagnostics for Population Size Estimation Model Fits

Description

Usage

Arguments

Details

References

See Also

Examples

Warning message for posteriorsize fit failure

Description

Usage

Value

See Also

Compute the posterior predictive p-values for the reported network sizes

Description

Usage

Arguments

Details

References

See Also

Examples

Estimating hidden population size using RDS data

Description

Usage

Arguments

Value

Details on priors

References

See Also

Examples

Summarizing Population Size Estimation Model Fits

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Summarizing Population Size Estimation Model Fits

Description

Usage

Arguments

Details

Value

See Also

Examples