# RDS.I.estimates: Compute RDS-I Estimates In RDS: Respondent-Driven Sampling

## Description

This function computes the RDS-I type estimates for a categorical variable. It is also referred to as the Salganik-Heckathorn estimator.

## Usage

 ```1 2 3``` ```RDS.I.estimates(rds.data, outcome.variable, N = NULL, subset = NULL, smoothed = FALSE, empir.lik = TRUE, to.factor = FALSE, cont.breaks = 3) ```

## Arguments

 `rds.data` An `rds.data.frame` that indicates recruitment patterns by a pair of attributes named “id” and “recruiter.id”. `outcome.variable` A string giving the name of the variable in the `rds.data` that contains a categorical variable to be analyzed. `N` Population size to be used to calculate the empirical likelihood interval. If NULL, this value is taken to be the population.size.mid attribute of the data and if that is not set, no finite population correction is used. `subset` An expression defining a subset of rds.data. `smoothed` Logical, if TRUE then the “data smoothed” version of RDS-I is used, where it is assumed that the observed Markov process is reversible. `empir.lik` Should confidence intervals be estimated using empirical likelihood. `to.factor` force variable to be a factor `cont.breaks` The number of categories used for the RDS-I adjustment when the variate is continuous.

## Value

If the `empir.lik` is true, an object of class `rds.interval.estimate` is returned. This is a list with components

• `estimate`: The numerical point estimate of proportion of the `trait.variable`.

• `interval`: A matrix with six columns and one row per category of `trait.variable`:

• `point estimate`: The HT estimate of the population mean.

• `95% Lower Bound`: Lower 95% confidence bound.

• ```95% Upper Bound```: Upper 95% confidence bound.

• `Design Effect`: The design effect of the RDS.

• `s.e.`: Standard error.

• `n`: Count of the number of sample values with that value of the trait.

Otherwise an object of class `rds.I.estimate` object is returned.

## Author(s)

Mark S. Handcock and W. Whipple Neely

## References

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

Neely, W. W., 2009. Bayesian methods for data from respondent driven sampling. Dissertation in-progress, Department of Statistics, University of Wisconsin, Madison.

Salganik, M., Heckathorn, D. D., 2004. Sampling and estimation in hidden populations using respondent-driven sampling. Sociological Methodology 34, 193-239.

Volz, E., Heckathorn, D., 2008. Probability based estimation theory for Respondent Driven Sampling. The Journal of Official Statistics 24 (1), 79-97.

`RDS.II.estimates`, `RDS.SS.estimates`
 ```1 2 3``` ```data(faux) RDS.I.estimates(rds.data=faux,outcome.variable='X') RDS.I.estimates(rds.data=faux,outcome.variable='X',smoothed=TRUE) ```