Last data update: 2014.03.03

 R: Longitudinal classroom friendship network and behavior...
knechtR Documentation

Longitudinal classroom friendship network and behavior (Andrea Knecht)

Description

The Knecht dataset contains the friendship network of 26 pupils in a Dutch school class measured at four time points along with several demographic and behavioral covariates like age, sex, ethnicity, religion, delinquency, alcohol consumption, primary school co-attendance, and school advice. Some of these covariates are constant while others vary over time.

The full dataset (see Knecht 2006 and 2008) contains a large number of classrooms while the dataset presented here is an excerpt based on one single classroom. This excerpt was first used in a tutorial for the software Siena and the corresponding R package RSiena (Snijders, Steglich and van de Bunt 2010). The following description was largely copied from the original data description provided on the homepage of the Siena project (see below for the URL).

The data were collected between September 2003 and June 2004 by Andrea Knecht, supervised by Chris Baerveldt, at the Department of Sociology of the University of Utrecht (NL). The entire study is reported in Knecht (2008). The project was funded by the Netherlands Organisation for Scientific Research NWO, grant 401-01-554. The 26 students were followed over their first year at secondary school during which friendship networks as well as other data were assessed at four time points at intervals of three months. There were 17 girls and 9 boys in the class, aged 11–13 at the beginning of the school year. Network data were assessed by asking students to indicate up to twelve classmates which they considered good friends. Delinquency is defined as a rounded average over four types of minor delinquency (stealing, vandalism, graffiti, and fighting), measured in each of the four waves of data collection. The five-point scale ranged from ‘never’ to 'more than 10 times', and the distribution is highly skewed. In a range of 1–5, the mode was 1 at all four waves, the average rose over time from 1.4 to 2.0, and the value 5 was never observed.

Usage

data(knecht)

Format

Note: the data have to be transformed before they can be used with btergm and related packages (see examples below).

friendship

is a list of adjacency matrices at four time points, containing friendship nominations of the column node by the row node. The following values are used: 0 = no, 1 = yes, NA = missing, 10 = not a member of the classroom (structural zero).

demographics

is a data frame with 26 rows (the pupils) and four demographic variables about the pupils:

  • sex (1 = girl, 2 = boy)

  • age (in years)

  • ethnicity (1 = Dutch, 2 = other, 0 = missing)

  • religion (1 = Christian, 2 = non-religious, 3 = non-Christian religion, 0 = missing)

primary

is a 26 x 26 matrix indicating whether two pupils attended the same primary school. 0 = no, 1 = yes.

delinquency

is a data frame with 26 rows (the pupils) and four columns (the four time steps). It contains the rounded average of four items (stealing, vandalizing, fighting, graffiti). Categories: frequency over last three months, 1 = never, 2 = once, 3 = 2–4 times, 4 = 5–10 times, 5 = more than 10 times; 0 = missing.

alcohol

is a data frame with 26 rows (the pupils) and 3 columns (waves 2, 3, and 4). It contains data on alcohol use (“How often did you drink alcohol with friends in the last three months?”). Categories: 1 = never, 2 = once, 3 = 2–4 times, 4 = 5–10 times, 5 = more than 10 times; 0 = missing.

advice

is a data frame with one variable, “school advice”, the assessment given at the end of primary school about the school capabilities of the pupil (4 = low, 8 = high, 0 = missing)

Source

The data were gathered by Andrea Knecht, as part of her PhD research, building on methods developed by Chris Baerveldt, initiator and supervisor of the project. The project is funded by the Netherlands Organisation for Scientific Research NWO, grant 401-01-554, and is part of the research program “Dynamics of Networks and Behavior” with principle investigator Tom A. B. Snijders.

Permission to redistribute this dataset along with this package was granted by Andrea Knecht on April 17, 2014. Questions about the data or the original study should be directed to her.

References

Knecht, Andrea (2006): Networks and Actor Attributes in Early Adolescence [2003/04]. Utrecht, The Netherlands Research School ICS, Department of Sociology, Utrecht University. (ICS-Codebook no. 61).

Knecht, Andrea (2008): Friendship Selection and Friends' Influence. Dynamics of Networks and Actor Attributes in Early Adolescence. PhD Dissertation, University of Utrecht. http://dspace.library.uu.nl/bitstream/handle/1874/25950/full.pdf.

Knecht, Andrea, Tom A. B. Snijders, Chris Baerveldt, Christian E. G. Steglich, and Werner Raub (2010): Friendship and Delinquency: Selection and Influence Processes in Early Adolescence. Social Development 19(3): 494–514. http://dx.doi.org/10.1111/j.1467-9507.2009.00564.x.

Leifeld, Philip and Skyler J. Cranmer (2014): Comparing the Temporal Exponential Random Graph Model (TERGM) and the Stochastic Actor-Oriented Model (SAOM). Paper presented at the 2014 Annual Meeting of the Swiss Political Science Association (SVPW), Bern, Switzerland, January 30.

Snijders, Tom A. B., Christian E. G. Steglich, and Gerhard G. van de Bunt (2010): Introduction to Actor-Based Models for Network Dynamics. Social Networks 32: 44–60. http://dx.doi.org/10.1016/j.socnet.2009.02.004.

Steglich, Christian E. G. and Andrea Knecht (2009): Die statistische Analyse dynamischer Netzwerkdaten. In: Stegbauer, Christian and Roger Haeussling (editors), Handbuch der Netzwerkforschung, Wiesbaden: Verlag fuer Sozialwissenschaften.

Examples

## Not run: 
require("texreg")
require("sna")
require("xergm")
require("RSiena")
data("knecht")

# what do the networks look like? plot them!
par(mfrow = c(2, 2), mar = c(0, 0, 1, 0))
for (i in 1:length(friendship)) {
  plot(network(friendship[[i]]), main = paste("t =", i), 
      usearrows = FALSE, edge.col = "grey50")
}

# ====================================================================
# Preprocess data and estimate TERGMs using the btergm function
# ====================================================================

# first, estimate a temporally pooled ERGM

# the Knecht network has the same dimensions at all time steps; "10" 
# values indicate composition change; NA values are missings

# step 1: make sure the network matrices have node labels
for (i in 1:length(friendship)) {
  rownames(friendship[[i]]) <- 1:nrow(friendship[[i]])
  colnames(friendship[[i]]) <- 1:ncol(friendship[[i]])
}
rownames(primary) <- rownames(friendship[[1]])
colnames(primary) <- colnames(friendship[[1]])

# step 2: preprocess dep. NW, remove struct. zeros, impute NA with 0:
# get rid of missing data in the friendship networks (the "dependent 
# variable") and adjust the dimensions temporally

dep <- preprocess(friendship, primary, demographics$sex, lag = FALSE, 
    covariate = FALSE, na = NA, na.method = "fillmode", 
    structzero = 10, structzero.method = "remove")
    # this has to be repeated for the covariates if they have NAs

length(dep)              # make sure there are still four time steps
sapply(friendship, dim)  # network dimensions: 26-26-26-26
sapply(dep, dim)         # after the adjustment: 26-26-25-25
rownames(dep[[3]])       # node 21 (an NA value) was removed

# step 3: preprocess covariates; adjust them to the "dep" dimensions

primary.cov <- preprocess(primary, dep, demographics$sex, 
    lag = FALSE, covariate = TRUE)
sex.cov <- preprocess(demographics$sex, primary.cov, dep, 
    lag = FALSE, covariate = TRUE)

sapply(primary.cov, dim)      # 26-26-25-25
sapply(sex.cov, length)       # 26-26-25-25

# step 4: add nodal covariates to the networks
for (i in 1:length(dep)) {
  dep[[i]] <- network(dep[[i]])
  odegsqrt <- sqrt(degree(dep[[i]], cmode = "outdegree"))
  idegsqrt <- sqrt(degree(dep[[i]], cmode = "indegree"))
  dep[[i]] <- set.vertex.attribute(dep[[i]], "odegsqrt", odegsqrt)
  dep[[i]] <- set.vertex.attribute(dep[[i]], "idegsqrt", idegsqrt)
  dep[[i]] <- set.vertex.attribute(dep[[i]], "sex", 
      sex.cov[[i]])
}

# step 5: estimate the TERGM without any lagged terms
model1 <- btergm(dep ~ edges + mutual + ttriple + transitiveties + 
    ctriple + nodeicov("idegsqrt") + nodeicov("odegsqrt") + 
    nodeocov("odegsqrt") + nodeofactor("sex") + nodeifactor("sex") + 
    nodematch("sex") + edgecov(primary.cov), R = 100)

summary(model1, level = 0.95)  # look at the results of the estimation

# step 5: plot goodness of fit (see ?gof.btergm and ?plot.btergmgof)
gof1 <- gof(model1, nsim = 25)
plot(gof1)  # display boxplot diagram


# ====================================================================
# Add cross-temporal dynamics
# ====================================================================

# we now include cross-temporal dynamics

# step 1: preprocess data; this time with a lag
# dep contains t = 2 to t = 4
# lag contains t = 1 to t = 3
# mem indicates edge stability between 1-2, 2-3, and 3-4
dep <- preprocess(friendship, primary, demographics$sex, lag = TRUE, 
    covariate = FALSE, na = NA, na.method = "fillmode", 
    structzero = 10, structzero.method = "remove")
lag <- preprocess(friendship, primary, demographics$sex, lag = TRUE, 
    covariate = TRUE, na = NA, na.method = "fillmode", 
    structzero = 10, structzero.method = "remove")
mem <- preprocess(friendship, primary, demographics$sex, lag = TRUE, 
    covariate = TRUE, memory = "stability", na = NA, 
    na.method = "fillmode", structzero = 10, 
    structzero.method = "remove")
primary.cov <- preprocess(primary, dep, demographics$sex, 
    lag = FALSE, covariate = TRUE)
sex.cov <- preprocess(demographics$sex, primary.cov, dep, 
    lag = FALSE, covariate = TRUE)

length(dep)       # now there are only three time steps
sapply(dep, dim)  # after the adjustment: 26-25-25
sapply(lag, dim)  # 26-25-25
sapply(mem, dim)  # 26-25-25 (stability between t and t - 1)

# delayed reciprocity: are ties from t - 1 reciprocated at t?
delrecip <- lapply(friendship, t)  # transpose friendship matrices
delrecip <- preprocess(delrecip, primary, friendship, lag = TRUE, 
    covariate = TRUE, na = NA, na.method = "fillmode", 
    structzero = 10, structzero.method = "remove")
sapply(delrecip, dim)

# step 3: add nodal covariates to the networks
for (i in 1:length(dep)) {
  dep[[i]] <- network(dep[[i]])
  odegsqrt <- sqrt(degree(dep[[i]], cmode = "outdegree"))
  idegsqrt <- sqrt(degree(dep[[i]], cmode = "indegree"))
  dep[[i]] <- set.vertex.attribute(dep[[i]], "odegsqrt", odegsqrt)
  dep[[i]] <- set.vertex.attribute(dep[[i]], "idegsqrt", idegsqrt)
  dep[[i]] <- set.vertex.attribute(dep[[i]], "sex", sex.cov[[i]])
}

# step 4: estimate the TERGM with cross-temporal model terms
model2 <- btergm(dep ~ edges + mutual + ttriple + transitiveties + 
    ctriple + nodeicov("idegsqrt") + nodeicov("odegsqrt") + 
    nodeocov("odegsqrt") + nodeofactor("sex") + nodeifactor("sex") + 
    nodematch("sex") + edgecov(primary.cov) + edgecov(delrecip) + 
    edgecov(mem), R = 100)

# look at the results (first using tables, then visually)
summary(model2)
screenreg(list(model1, model2))  # compare the two models directly
plotreg(model2, custom.model.names = "Model 2", custom.coef.names = 
    c("Edges", "Reciprocity", "Transitive triples", 
    "Transitive ties", "Cyclic triples", "Indegree popularity", 
    "Outdegree popularity", "Outdegree activity", "Ego = male", 
    "Alter = male", "Both nodes = male", "Same primary school", 
    "Delayed reciprocity", "Memory term (edge stability)"), 
    omit.coef = "Edges", file="coefs.pdf")

# step 5: plot goodness of fit (see ?gof.btergm and ?plot.btergmgof)
gof2 <- gof(model2, nsim = 25)
plot(gof2)  # display boxplot diagram; model fit is much better now!


# ====================================================================
# assess out-of-sample predictive performance of the model
# ====================================================================

# we also want to try to predict the network at t = 4 based on a model
# estimated for t = 1 through t = 3
model3 <- btergm(dep[1:2] ~ edges + mutual + ttriple + transitiveties + 
    ctriple + nodeicov("idegsqrt") + nodeicov("odegsqrt") + 
    nodeocov("odegsqrt") + nodeofactor("sex") + nodeifactor("sex") + 
    nodematch("sex") + edgecov(primary.cov[1:2]) + edgecov(delrecip[1:2]) + 
    edgecov(mem[1:2]), R = 100)

screenreg(list(model1, model2, model3))  # similar results as before

# simulate 100 networks from t = 3 and compare to t = 4    
gof3 <- gof(model3, nsim = 100, target = dep[[3]], formula = dep[[3]] ~ 
    edges + mutual + ttriple + transitiveties + ctriple + 
    nodeicov("idegsqrt") + nodeicov("odegsqrt") + 
    nodeocov("odegsqrt") + nodeofactor("sex") + nodeifactor("sex") + 
    nodematch("sex") + edgecov(primary.cov[[3]]) + 
    edgecov(delrecip[[3]]) + edgecov(mem[[3]]))

# display goodness of fit
plot(gof3, roc = FALSE, pr = FALSE)  # predictive fit (boxplots)
gof3  # display goodness of fit tables
pdf("rocpr.pdf")
plot(gof3, boxplot = FALSE, pr = FALSE, roc = TRUE, 
    roc.random = TRUE, pr.random = FALSE, ylab = "TPR/PPV", 
    xlab = "FPR/TPR", roc.main = "ROC and PR curves")  # ROC curve
plot(gof3, boxplot = FALSE, roc = FALSE, pr = TRUE, 
    pr.random = TRUE, rocpr.add = TRUE)  # add PR curve
dev.off()

# ====================================================================
# assess predictive goodness of fit of a SAOM (estimated using RSiena)
# ====================================================================

# determine composition change
comp <- rep(list(c(1, 4)), 26)  # actors are present from t=1 to t=4
comp[[21]] <- c(1, 2)  # actor 21 drops out after the second time step
changes <- sienaCompositionChange(comp)

# prepare networks and covariate model terms
siena.nets <- sienaNet(array(c(friendship[[1]], friendship[[2]], 
    friendship[[3]], friendship[[4]]), dim = c(26, 26, 4)))
primaryCov <- coDyadCovar(primary)
sexCov <- coCovar(demographics$sex)
ageCov <- coCovar(demographics$age)
ethnicityCov <- coCovar(demographics$ethnicity)
religionCov <- coCovar(demographics$religion)

mymodel <- sienaModelCreate(useStdInits = FALSE, projname = "myproject")

mydata <- sienaDataCreate(siena.nets, primaryCov, sexCov, ageCov, 
    ethnicityCov, religionCov, changes)

# add effects
myeff <- getEffects(mydata)
myeff <- includeEffects(myeff, transTrip)
myeff <- includeEffects(myeff, transTies)
myeff <- includeEffects(myeff, cycle3)
myeff <- includeEffects(myeff, outPopSqrt)
myeff <- includeEffects(myeff, egoX, interaction1 = "sexCov")
myeff <- includeEffects(myeff, altX, interaction1 = "sexCov")
myeff <- includeEffects(myeff, sameX, interaction1 = "sexCov")
myeff <- includeEffects(myeff, X, interaction1 = "primaryCov")
myeff <- includeEffects(myeff, inPopSqrt)
myeff <- includeEffects(myeff, outActSqrt)

# estimate the SIENA model
ans <- siena07(mymodel, data = mydata, effects = myeff, batch = TRUE, 
    verbose = FALSE)
ans  # display results

# finally, assess predictive performance of the model using the btergm 
# package; this should take up to 10 minutes on a recent PC
siena.gof <- gof(
    mymodel,                     # hand over the SIENA model
    siena.data = mydata,         # ... and the SIENA data
    siena.effects = myeff,       # ... and the SIENA effects
    nsim = 3,                    # number of estimation replications
                                 # (should be 100, but is very slow!)
    target.na = NA,              # how are NA values denoted?
    target.na.method = "remove", # remove NAs in comparison network
    target.structzero = 10,      # how are structural zeros denoted?
    parallel = "no",             # adjust this for parallel processing
    ncpus = 1                    # number of CPU cores
)

siena.gof  # display goodness of fit results

# plot the goodness of fit (see ?gof.btergmgof for details)
plot(siena.gof, roc = FALSE, pr = FALSE)  # display boxplot diagram
plot(siena.gof, boxplot = FALSE, pr = FALSE)  # display ROC curve
plot(siena.gof, boxplot = FALSE, roc = FALSE)  # display PR curve

# compare ROC and PR curves for TERGM and SAOM
plot(siena.gof, boxplot = FALSE, pr = FALSE, roc.col = "red1", 
    ylab = "", xlab = "", roc.main = "SAOM versus TERGM prediction")
plot(siena.gof, boxplot = FALSE, roc = FALSE, pr.col = "steelblue1", 
    rocpr.add = TRUE)
plot(gof3, boxplot = FALSE, pr = FALSE, roc.col = "red4", 
    rocpr.add = TRUE)
plot(gof3, boxplot = FALSE, roc = FALSE, pr.col = "steelblue4", 
    rocpr.add = TRUE)
color <- c("red1", "red4", "steelblue1", "steelblue4")
label <- c("SAOM ROC", "TERGM ROC", "SAOM PR", "TERGM PR")
legend("bottom", legend = label, col = color, lty = 1, lwd = 3)

# compare area under the curve
ROC <- c(SAOM = siena.gof$auc.roc, TERGM = gof3$auc.roc)
PR <- c(SAOM = siena.gof$auc.pr, TERGM = gof3$auc.pr)
barplot(cbind(ROC, PR), beside = TRUE, col = color)
legend("topright", legend = label, pch = 15, col = color)


## End(Not run)

Results


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