R/bgof.R
In acaimo/Bergm: Bayesian Exponential Random Graph Models
Defines functions
bgof
Documented in
bgof
#' Bayesian goodness-of-fit diagnostics for ERGMs
#'
#' Function to calculate summaries for degree,
#' minimum geodesic distances,
#' and edge-wise shared partner distributions
#' to diagnose the Bayesian goodness-of-fit of
#' exponential random graph models.
#'
#' @param x an \code{R} object of class \code{bergm}.
#'
#' @param sample.size count; number of networks
#' to be simulated and compared to the observed network.
#'
#' @param aux.iters count; number of iterations used for network simulation.
#'
#' @param n.deg count; used to plot only the first
#' \code{n.deg}-1 degree distributions.
#' By default no restrictions on the number of degree
#' distributions is applied.
#'
#' @param n.dist count; used to plot only the first
#' \code{n.dist}-1 geodesic distances distributions.
#' By default no restrictions on the number of geodesic
#' distances distributions is applied.
#'
#' @param n.esp count; used to plot only the first
#' \code{n.esp}-1 edge-wise shared partner distributions.
#' By default no restrictions on the number of
#' edge-wise shared partner distributions is applied.
#'
#' @param n.ideg count; used to plot only the first
#' \code{n.ideg}-1 in-degree distributions.
#' By default no restrictions on the number of
#' in-degree distributions is applied.
#'
#' @param n.odeg count; used to plot only the first
#' \code{n.odeg}-1 out-degree distributions.
#' By default no restrictions on the number of
#' out-degree distributions is applied.
#'
#' @param ... additional arguments,
#' to be passed to lower-level functions.
#'
#' @references
#' Caimo, A. and Friel, N. (2011), "Bayesian Inference for Exponential Random Graph Models,"
#' Social Networks, 33(1), 41-55. \url{https://arxiv.org/abs/1007.5192}
#'
#' Caimo, A. and Friel, N. (2014), "Bergm: Bayesian Exponential Random Graphs in R,"
#' Journal of Statistical Software, 61(2), 1-25. \url{https://www.jstatsoft.org/v61/i02}
#'
#' @examples
#' \dontrun{
#' # Load the florentine marriage network
#' data(florentine)
#'
#' # Posterior parameter estimation:
#' p.flo <- bergm(flomarriage ~ edges + kstar(2),
#' burn.in = 50,
#' aux.iters = 500,
#' main.iters = 1000,
#' gamma = 1.2)
#'
#' # Bayesian goodness-of-fit test:
#' bgof(p.flo,
#' aux.iters = 500,
#' sample.size = 30,
#' n.deg = 10,
#' n.dist = 9,
#' n.esp = 6)
#'}
#' @export
#'
bgof <- function(x,
sample.size = 100,
aux.iters = 10000,
n.deg = NULL,
n.dist = NULL,
n.esp = NULL,
n.ideg = NULL,
n.odeg = NULL,
...){
FF <- as.matrix(x$Theta[sample(dim(x$Theta)[1], sample.size), ])
DN <- is.directed(ergm.getnetwork(x$formula))
if (DN == FALSE) { # undirected
for (i in 1:sample.size) {
a <- gof(x$formula,
coef = FF[i, ],
verbose = FALSE,
control = control.gof.formula(nsim = 2,
MCMC.burnin = aux.iters,
MCMC.interval = 1))
if (i == 1) A <- as.vector(a$pobs.deg)
A <- cbind(A, as.vector(a$psim.deg[2, ]))
if (i == 1) B <- as.vector(a$pobs.dist)
B <- cbind(B,as.vector(a$psim.dist[2, ]))
if (i == 1) C <- as.vector(a$pobs.espart)
C <- cbind(C,as.vector(a$psim.espart[2, ]))
}
if (is.null(n.deg)) n.deg <- dim(A)[1]
if (is.null(n.dist)) n.dist <- dim(B)[1] - 1
if (is.null(n.esp)) n.esp <- dim(C)[1]
a5 <- apply(A[1:n.deg, -1],
1, quantile, probs = 0.05)
b5 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1],
1, quantile, probs = 0.05)
c5 <- apply(C[1:n.esp, -1],
1, quantile, probs = 0.05)
a95 <- apply(A[1:n.deg, -1],
1, quantile, probs = 0.95)
b95 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1],
1, quantile, probs = 0.95)
c95 <- apply(C[1:n.esp, -1],
1, quantile, probs = 0.95)
par(mfrow = c(1, 3), oma = c(0, 0, 3, 0), mar = c(4, 3, 1.5, 1))
boxplot(as.data.frame(t(A[1:n.deg, -1])),
xaxt = "n",
xlab = "degree",
ylab = "proportion of nodes")
axis(1, seq(1, n.deg), seq(0, n.deg - 1))
lines(A[1:n.deg, 1], lwd = 2, col = 2)
lines(a5, col = "darkgray")
lines(a95, col = "darkgray")
title("Bayesian goodness-of-fit diagnostics", outer = TRUE)
boxplot(as.data.frame(t(B[-(n.dist:(dim(B)[1] - 1)), -1])),
xaxt = "n",
xlab = "minimum geodesic distance",
ylab = "proportion of dyads")
axis(1, seq(1, n.dist), labels = c(seq(1, (n.dist - 1)), "NR"))
lines(B[-(n.dist:(dim(B)[1] - 1)), 1],lwd = 2, col = 2)
lines(b5, col = "darkgray")
lines(b95, col = "darkgray")
boxplot(as.data.frame(t(C[1:n.esp,-1])),
xaxt = "n",
xlab = "edge-wise shared partners",
ylab = "proportion of edges")
axis(1,seq(1, n.esp),seq(0, n.esp - 1))
lines(C[1:n.esp, 1],lwd = 2,col = 2)
lines(c5,col = "darkgray")
lines(c95,col = "darkgray")
out = list(sim.degree = A[,-1],
sim.dist = B[,-1],
sim.esp = C[,-1],
obs.degree = A[,1],
obs.dist = B[,1],
obs.esp = C[,1])
} else {# directed
for (i in 1:sample.size) {
a <- gof(x$formula,
coef = FF[i,],
verbose = FALSE,
GOF = ~ idegree + odegree + espartners + distance,
control = control.gof.formula(nsim = 2,
MCMC.burnin = aux.iters,
MCMC.interval = 1))
if (i == 1) A <- as.vector(a$pobs.ideg)
A <- cbind(A, as.vector(a$psim.ideg[2, ]))
if (i == 1) AA <- as.vector(a$pobs.odeg)
AA <- cbind(AA, as.vector(a$psim.odeg[2, ]))
if (i == 1) B <- as.vector(a$pobs.dist)
B <- cbind(B, as.vector(a$psim.dist[2, ]))
if (i == 1) C <- as.vector(a$pobs.espart)
C <- cbind(C, as.vector(a$psim.espart[2, ]))
}
if (is.null(n.ideg)) n.ideg <- dim(A)[1]
if (is.null(n.odeg)) n.odeg <- dim(AA)[1]
if (is.null(n.dist)) n.dist <- dim(B)[1] - 1
if (is.null(n.esp)) n.esp <- dim(C)[1]
a5 <- apply(A[1:n.ideg, -1], 1, quantile, probs = 0.05)
aa5 <- apply(AA[1:n.odeg, -1], 1, quantile, probs = 0.05)
b5 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1], 1, quantile, probs = 0.05)
c5 <- apply(C[1:n.esp, -1], 1, quantile, probs = 0.05)
a95 <- apply(A[1:n.ideg, -1], 1, quantile, probs = 0.95)
aa95 <- apply(AA[1:n.odeg, -1], 1, quantile, probs = 0.95)
b95 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1], 1, quantile, probs = 0.95)
c95 <- apply(C[1:n.esp, -1], 1, quantile, probs = 0.95)
par(mfrow = c(2, 2), oma = c(0, 0, 3, 0), mar = c(4, 3, 1.5, 1))
boxplot(as.data.frame(t(A[1:n.ideg,-1])),
xaxt = "n",
xlab = "in degree",
ylab = "proportion of nodes")
axis(1, seq(1, n.ideg), seq(0, n.ideg - 1))
lines(A[1:n.ideg, 1], lwd = 2, col = 2)
lines(a5, col = "darkgray")
lines(a95, col = "darkgray")
title("Bayesian goodness-of-fit diagnostics", outer = TRUE)
boxplot(as.data.frame(t(AA[1:n.odeg, -1])),
xaxt = "n",
xlab = "out degree",
ylab = "proportion of nodes")
axis(1,seq(1, n.odeg),seq(0, n.odeg - 1))
lines(AA[1:n.odeg, 1],lwd = 2,col = 2)
lines(aa5, col = "darkgray")
lines(aa95, col = "darkgray")
boxplot(as.data.frame(t(B[-(n.dist:(dim(B)[1] - 1)), -1])),
xaxt = "n",
xlab = "minimum geodesic distance",
ylab = "proportion of dyads")
axis(1, seq(1, n.dist), labels = c(seq(1, (n.dist - 1)), "NR"))
lines(B[-(n.dist:(dim(B)[1] - 1)), 1], lwd = 2 , col = 2)
lines(b5,col = "darkgray")
lines(b95,col = "darkgray")
boxplot(as.data.frame(t(C[1:n.esp, -1])),
xaxt = "n",
xlab = "edge-wise shared partners",
ylab = "proportion of edges")
axis(1, seq(1, n.esp), seq(0, n.esp - 1))
lines(C[1:n.esp, 1],lwd = 2, col = 2)
lines(c5, col = "darkgray")
lines(c95, col = "darkgray")
out = list(sim.idegree = A[,-1],
sim.odegree = AA[,-1],
sim.dist = B[,-1],
sim.esp = C[,-1],
obs.degree = A[,1],
obs.dist = B[,1],
obs.esp = C[,1])
}
}
acaimo/Bergm documentation built on Jan. 17, 2024, 2:36 p.m.
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Defines functions bgof
Documented in bgof
#' Bayesian goodness-of-fit diagnostics for ERGMs
#'
#' Function to calculate summaries for degree,
#' minimum geodesic distances,
#' and edge-wise shared partner distributions
#' to diagnose the Bayesian goodness-of-fit of
#' exponential random graph models.
#'
#' @param x an \code{R} object of class \code{bergm}.
#'
#' @param sample.size count; number of networks
#' to be simulated and compared to the observed network.
#'
#' @param aux.iters count; number of iterations used for network simulation.
#'
#' @param n.deg count; used to plot only the first
#' \code{n.deg}-1 degree distributions.
#' By default no restrictions on the number of degree
#' distributions is applied.
#'
#' @param n.dist count; used to plot only the first
#' \code{n.dist}-1 geodesic distances distributions.
#' By default no restrictions on the number of geodesic
#' distances distributions is applied.
#'
#' @param n.esp count; used to plot only the first
#' \code{n.esp}-1 edge-wise shared partner distributions.
#' By default no restrictions on the number of
#' edge-wise shared partner distributions is applied.
#'
#' @param n.ideg count; used to plot only the first
#' \code{n.ideg}-1 in-degree distributions.
#' By default no restrictions on the number of
#' in-degree distributions is applied.
#'
#' @param n.odeg count; used to plot only the first
#' \code{n.odeg}-1 out-degree distributions.
#' By default no restrictions on the number of
#' out-degree distributions is applied.
#'
#' @param ... additional arguments,
#' to be passed to lower-level functions.
#'
#' @references
#' Caimo, A. and Friel, N. (2011), "Bayesian Inference for Exponential Random Graph Models,"
#' Social Networks, 33(1), 41-55. \url{https://arxiv.org/abs/1007.5192}
#'
#' Caimo, A. and Friel, N. (2014), "Bergm: Bayesian Exponential Random Graphs in R,"
#' Journal of Statistical Software, 61(2), 1-25. \url{https://www.jstatsoft.org/v61/i02}
#'
#' @examples
#' \dontrun{
#' # Load the florentine marriage network
#' data(florentine)
#'
#' # Posterior parameter estimation:
#' p.flo <- bergm(flomarriage ~ edges + kstar(2),
#' burn.in = 50,
#' aux.iters = 500,
#' main.iters = 1000,
#' gamma = 1.2)
#'
#' # Bayesian goodness-of-fit test:
#' bgof(p.flo,
#' aux.iters = 500,
#' sample.size = 30,
#' n.deg = 10,
#' n.dist = 9,
#' n.esp = 6)
#'}
#' @export
#'
bgof <- function(x,
sample.size = 100,
aux.iters = 10000,
n.deg = NULL,
n.dist = NULL,
n.esp = NULL,
n.ideg = NULL,
n.odeg = NULL,
...){
FF <- as.matrix(x$Theta[sample(dim(x$Theta)[1], sample.size), ])
DN <- is.directed(ergm.getnetwork(x$formula))
if (DN == FALSE) { # undirected
for (i in 1:sample.size) {
a <- gof(x$formula,
coef = FF[i, ],
verbose = FALSE,
control = control.gof.formula(nsim = 2,
MCMC.burnin = aux.iters,
MCMC.interval = 1))
if (i == 1) A <- as.vector(a$pobs.deg)
A <- cbind(A, as.vector(a$psim.deg[2, ]))
if (i == 1) B <- as.vector(a$pobs.dist)
B <- cbind(B,as.vector(a$psim.dist[2, ]))
if (i == 1) C <- as.vector(a$pobs.espart)
C <- cbind(C,as.vector(a$psim.espart[2, ]))
}
if (is.null(n.deg)) n.deg <- dim(A)[1]
if (is.null(n.dist)) n.dist <- dim(B)[1] - 1
if (is.null(n.esp)) n.esp <- dim(C)[1]
a5 <- apply(A[1:n.deg, -1],
1, quantile, probs = 0.05)
b5 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1],
1, quantile, probs = 0.05)
c5 <- apply(C[1:n.esp, -1],
1, quantile, probs = 0.05)
a95 <- apply(A[1:n.deg, -1],
1, quantile, probs = 0.95)
b95 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1],
1, quantile, probs = 0.95)
c95 <- apply(C[1:n.esp, -1],
1, quantile, probs = 0.95)
par(mfrow = c(1, 3), oma = c(0, 0, 3, 0), mar = c(4, 3, 1.5, 1))
boxplot(as.data.frame(t(A[1:n.deg, -1])),
xaxt = "n",
xlab = "degree",
ylab = "proportion of nodes")
axis(1, seq(1, n.deg), seq(0, n.deg - 1))
lines(A[1:n.deg, 1], lwd = 2, col = 2)
lines(a5, col = "darkgray")
lines(a95, col = "darkgray")
title("Bayesian goodness-of-fit diagnostics", outer = TRUE)
boxplot(as.data.frame(t(B[-(n.dist:(dim(B)[1] - 1)), -1])),
xaxt = "n",
xlab = "minimum geodesic distance",
ylab = "proportion of dyads")
axis(1, seq(1, n.dist), labels = c(seq(1, (n.dist - 1)), "NR"))
lines(B[-(n.dist:(dim(B)[1] - 1)), 1],lwd = 2, col = 2)
lines(b5, col = "darkgray")
lines(b95, col = "darkgray")
boxplot(as.data.frame(t(C[1:n.esp,-1])),
xaxt = "n",
xlab = "edge-wise shared partners",
ylab = "proportion of edges")
axis(1,seq(1, n.esp),seq(0, n.esp - 1))
lines(C[1:n.esp, 1],lwd = 2,col = 2)
lines(c5,col = "darkgray")
lines(c95,col = "darkgray")
out = list(sim.degree = A[,-1],
sim.dist = B[,-1],
sim.esp = C[,-1],
obs.degree = A[,1],
obs.dist = B[,1],
obs.esp = C[,1])
} else {# directed
for (i in 1:sample.size) {
a <- gof(x$formula,
coef = FF[i,],
verbose = FALSE,
GOF = ~ idegree + odegree + espartners + distance,
control = control.gof.formula(nsim = 2,
MCMC.burnin = aux.iters,
MCMC.interval = 1))
if (i == 1) A <- as.vector(a$pobs.ideg)
A <- cbind(A, as.vector(a$psim.ideg[2, ]))
if (i == 1) AA <- as.vector(a$pobs.odeg)
AA <- cbind(AA, as.vector(a$psim.odeg[2, ]))
if (i == 1) B <- as.vector(a$pobs.dist)
B <- cbind(B, as.vector(a$psim.dist[2, ]))
if (i == 1) C <- as.vector(a$pobs.espart)
C <- cbind(C, as.vector(a$psim.espart[2, ]))
}
if (is.null(n.ideg)) n.ideg <- dim(A)[1]
if (is.null(n.odeg)) n.odeg <- dim(AA)[1]
if (is.null(n.dist)) n.dist <- dim(B)[1] - 1
if (is.null(n.esp)) n.esp <- dim(C)[1]
a5 <- apply(A[1:n.ideg, -1], 1, quantile, probs = 0.05)
aa5 <- apply(AA[1:n.odeg, -1], 1, quantile, probs = 0.05)
b5 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1], 1, quantile, probs = 0.05)
c5 <- apply(C[1:n.esp, -1], 1, quantile, probs = 0.05)
a95 <- apply(A[1:n.ideg, -1], 1, quantile, probs = 0.95)
aa95 <- apply(AA[1:n.odeg, -1], 1, quantile, probs = 0.95)
b95 <- apply(B[-(n.dist:(dim(B)[1] - 1)), -1], 1, quantile, probs = 0.95)
c95 <- apply(C[1:n.esp, -1], 1, quantile, probs = 0.95)
par(mfrow = c(2, 2), oma = c(0, 0, 3, 0), mar = c(4, 3, 1.5, 1))
boxplot(as.data.frame(t(A[1:n.ideg,-1])),
xaxt = "n",
xlab = "in degree",
ylab = "proportion of nodes")
axis(1, seq(1, n.ideg), seq(0, n.ideg - 1))
lines(A[1:n.ideg, 1], lwd = 2, col = 2)
lines(a5, col = "darkgray")
lines(a95, col = "darkgray")
title("Bayesian goodness-of-fit diagnostics", outer = TRUE)
boxplot(as.data.frame(t(AA[1:n.odeg, -1])),
xaxt = "n",
xlab = "out degree",
ylab = "proportion of nodes")
axis(1,seq(1, n.odeg),seq(0, n.odeg - 1))
lines(AA[1:n.odeg, 1],lwd = 2,col = 2)
lines(aa5, col = "darkgray")
lines(aa95, col = "darkgray")
boxplot(as.data.frame(t(B[-(n.dist:(dim(B)[1] - 1)), -1])),
xaxt = "n",
xlab = "minimum geodesic distance",
ylab = "proportion of dyads")
axis(1, seq(1, n.dist), labels = c(seq(1, (n.dist - 1)), "NR"))
lines(B[-(n.dist:(dim(B)[1] - 1)), 1], lwd = 2 , col = 2)
lines(b5,col = "darkgray")
lines(b95,col = "darkgray")
boxplot(as.data.frame(t(C[1:n.esp, -1])),
xaxt = "n",
xlab = "edge-wise shared partners",
ylab = "proportion of edges")
axis(1, seq(1, n.esp), seq(0, n.esp - 1))
lines(C[1:n.esp, 1],lwd = 2, col = 2)
lines(c5, col = "darkgray")
lines(c95, col = "darkgray")
out = list(sim.idegree = A[,-1],
sim.odegree = AA[,-1],
sim.dist = B[,-1],
sim.esp = C[,-1],
obs.degree = A[,1],
obs.dist = B[,1],
obs.esp = C[,1])
}
}
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