dissolution_coefs: Dissolution Coefficients for Stochastic Network Models

In EpiModel: Mathematical Modeling of Infectious Disease Dynamics

Dissolution Coefficients for Stochastic Network Models

Description

Calculates dissolution coefficients, given a dissolution model and average edge duration, to pass as offsets to an ERGM/TERGM model fit in netest.

Usage

dissolution_coefs(dissolution, duration, d.rate = 0)

Arguments

dissolution	Right-hand sided STERGM dissolution formula (see netest). See below for list of supported dissolution models.
duration	A vector of mean edge durations in arbitrary time units.
d.rate	Departure or exit rate from the population, as a single homogeneous rate that applies to the entire population.

Details

This function performs two calculations for dissolution coefficients used in a network model estimated with netest:

1. Transformation: the mean durations of edges in a network are mathematically transformed to logit coefficients.

2. Adjustment: in a dynamic network simulation in an open population (in which there are departures), it is further necessary to adjust these coefficients; this upward adjustment accounts for departure as a competing risk to edge dissolution.

The current dissolution models supported by this function and in network model estimation in netest are as follows:

• ~offset(edges): a homogeneous dissolution model in which the edge duration is the same for all partnerships. This requires specifying one duration value.

• ~offset(edges) + offset(nodematch("<attr>")): a heterogeneous model in which the edge duration varies by whether the nodes in the dyad have similar values of a specified attribute. The duration vector should now contain two values: the first is the mean edge duration of non-matched dyads, and the second is the duration of the matched dyads.

• ~offset(edges) + offset(nodemix("<attr>")): a heterogeneous model that extends the nodematch model to include non-binary attributes for homophily. The duration vector should first contain the base value, then the values for every other possible combination in the term.

Value

A list of class disscoef with the following elements:

• dissolution: right-hand sided STERGM dissolution formula passed in the function call.

• duration: mean edge durations passed into the function.

• coef.crude: mean durations transformed into logit coefficients.

• coef.adj: crude coefficients adjusted for the risk of departure on edge persistence, if the d.rate argument is supplied.

• coef.form.corr: corrections to be subtracted from formation coefficients.

• d.rate: the departure rate.

• diss.model.type: the form of the dissolution model; options include edgesonly, nodematch, and nodemix.

Examples

## Homogeneous dissolution model with no departures
dissolution_coefs(dissolution = ~offset(edges), duration = 25)

## Homogeneous dissolution model with departures
dissolution_coefs(dissolution = ~offset(edges), duration = 25,
                  d.rate = 0.001)

## Heterogeneous dissolution model in which same-race edges have
## shorter duration compared to mixed-race edges, with no departures
dissolution_coefs(dissolution = ~offset(edges) + offset(nodematch("race")),
                  duration = c(20, 10))

## Heterogeneous dissolution model in which same-race edges have
## shorter duration compared to mixed-race edges, with departures
dissolution_coefs(dissolution = ~offset(edges) + offset(nodematch("race")),
                  duration = c(20, 10), d.rate = 0.001)

## Not run: 
## Extended example for differential homophily by age group
# Set up the network with nodes categorized into 5 age groups
nw <- network_initialize(n = 1000)
age.grp <- sample(1:5, 1000, TRUE)
nw <- set_vertex_attribute(nw, "age.grp", age.grp)

# durations = non-matched, age.grp1 & age.grp1, age.grp2 & age.grp2, ...
# TERGM will include differential homophily by age group with nodematch term
# Target stats for the formation model are overall edges, and then the number
# matched within age.grp 1, age.grp 2, ..., age.grp 5
form <- ~edges + nodematch("age.grp", diff = TRUE)
target.stats <- c(450, 100, 125, 40, 80, 100)

# Target stats for the dissolution model are duration of non-matched edges,
# then duration of edges matched within age.grp 1, age.grp 2, ..., age.grp 5
durs <- c(60, 30, 80, 100, 125, 160)
diss <- dissolution_coefs(~offset(edges) +
                            offset(nodematch("age.grp", diff = TRUE)),
                          duration = durs)

# Fit the TERGM
fit <- netest(nw, form, target.stats, diss)

# Full diagnostics to evaluate model fit
dx <- netdx(fit, nsims = 10, ncores = 4, nsteps = 300)
print(dx)

# Simulate one long time series to examine timed edgelist
dx <- netdx(fit, nsims = 1, nsteps = 5000, keep.tedgelist = TRUE)

# Extract timed-edgelist
te <- as.data.frame(dx)
head(te)

# Limit to non-censored edges
te <- te[which(te$onset.censored == FALSE & te$terminus.censored == FALSE),
         c("head", "tail", "duration")]
head(te)

# Look up the age group of head and tail nodes
te$ag.head <- age.grp[te$head]
te$ag.tail <- age.grp[te$tail]
head(te)

# Recover average edge durations for age-group pairing
mean(te$duration[te$ag.head != te$ag.tail])
mean(te$duration[te$ag.head == 1 & te$ag.tail == 1])
mean(te$duration[te$ag.head == 2 & te$ag.tail == 2])
mean(te$duration[te$ag.head == 3 & te$ag.tail == 3])
mean(te$duration[te$ag.head == 4 & te$ag.tail == 4])
mean(te$duration[te$ag.head == 5 & te$ag.tail == 5])
durs

## End(Not run)

EpiModel documentation built on Oct. 12, 2024, 1:06 a.m.