RDS (version 0.8-1)

homophily.estimates: This function computes an estimate of the population homophily and the recruitment homophily based on a categorical variable.

Description

This function computes an estimate of the population homophily and the recruitment homophily based on a categorical variable.

Usage

homophily.estimates(rds.data, outcome.variable, weight.type = NULL,
  uncertainty = NULL, recruitment = FALSE, N = NULL,
  to.group0.variable = NULL, to.group1.variable = NULL,
  number.ss.samples.per.iteration = NULL, confidence.level = 0.95)

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 or numeric variable to be analyzed.

weight.type

A string giving the type of estimator to use. The options are "Gile's SS", "RDS-I", "RDS-II", "RDS-I/DS", "Good-Fellows" and "Arithemic Mean". If NULL it defaults to "Gile's SS".

uncertainty

A string giving the type of uncertainty estimator to use. The options are "Gile's SS" and "Salganik". This is usually determined by weight.type to be consistent with the estimator's origins (e.g., for "Gile's SS", "RDS-I", "RDS-II", "RDS-I/DS", and "Arithemic Mean"). Hence it's current functionality is limited. If NULL it defaults to "Gile's SS".

recruitment

A logical indicating if the homophily in the recruitment chains should be computed also. The default is FALSE.

N

An estimate of the number of members of the population being sampled. If NULL it is read as the population.size.mid attribute of the rds.data frame. If that is missing it defaults to 1000.

to.group0.variable

The number in the network of each survey respondent who have group variable value 0. Usually this is not available. The default is to not use this variable.

to.group1.variable

The number in the network of each survey respondent who have group variable value 1. Usually this is not available. The default is to not use this variable.

number.ss.samples.per.iteration

The number of samples to take in estimating the inclusion probabilites in each iteration of the sequential sampling algorithm. If NULL it is read as the number.ss.samples.per.iteration attribute of rds.data. If that is missing it defaults to 5000.

confidence.level

The confidence level for the confidence intervals. The default is 0.95 for 95%.

Value

If outcome.variable is binary then the homophily estimate of 0 verses 1 is returned, otherwise a vector of differential homophily estimates is returned.

Recruitment Homophily

The recruitment homophily is a homophily measure for the recruitment process. It addresses the question: Do respondents differential recruit people like themselves? That is, the homophily on a variable in the recruitment chains. Take as an example infection status. In this case, it is the ratio of number of recruits that have the same infection status as their recruiter to the number we would expect if there was no homophily on infection status. The difference with the Population Homophily (see below) is that this is in the recruitment chain rather than the population of social ties. For example, of the recruitment homophily on infection status is about 1, we see little effect of recruitment homophily on infection status (as the numbers of homophilous pairs are close to what we would expect by chance).

Population Homophily

This is an estimate the homophily of a given variable in the underlying networked population. For example, consider HIV status. The population homophily is the homophily in the HIV status of two people who are tied in the underlying population social network (a ``couple''). Specifically, the population homophily is the ratio of the expected number of HIV discordant couples absent homophily to the expected number of HIV discordant couples with the homophily. Hence larger values of population homophily indicate more homophily on HIV status. For example, a value of 1 means the couple are random with respect to HIV status. A value of 2 means there are twice as many HIV discordant couples as we would expect if there was no homophily in the population. This measure is meaningful across different levels of differential activity. As we do not see most of the population network, we estimate the population homophily from the RDS data. As an example, suppose the population homophily on HIV is 0.75 so there are 25% more HIV discordant couples than expected due to chance. So their is actually heterophily on HIV in the population. If the population homophily on sex is 1.1, there are 10% more same-sex couples than expected due to chance. Hence there is modest homophily on sex.

References

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

Examples

# NOT RUN {
data(fauxmadrona)
names(fauxmadrona)
#
# True value:
#
if(require(network)){
	a=as.sociomatrix(fauxmadrona.network)
	deg <- apply(a,1,sum)
	dis <- fauxmadrona.network \%v\% "disease"
	deg1 <- apply(a[dis==1,],1,sum)
	deg0 <- apply(a[dis==0,],1,sum)
	# differential activity
	mean(deg1)/ mean(deg0)
	p=mean(dis)
	N=1000
	# True homophily
	p*(1-p)*mean(deg0)*mean(deg1)*N/(mean(deg)*sum(a[dis==1,dis==0]))
}
# HT based estimators using the to.group information
data(fauxmadrona)
homophily.estimates(fauxmadrona,outcome.variable="disease",
  to.group0.variable="tonondiseased", to.group1.variable="todiseased",
  N=1000)
# HT based estimators not using the to.group information
homophily.estimates(fauxmadrona,outcome.variable="disease",
  N=1000,weight.type="RDS-II")
# }