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--- sna_eg_stanford:lab06 [2019/12/03 15:16] – hkimscil
+++ sna_eg_stanford:lab06 [2019/12/04 11:15] – hkimscil
@@ Line 39: / Line 39: @@
 library(NetCluster)
+# install.packages(c("sna", "NetCluster"))
 ###
 #2. LOADING AND FORMATTING DATA
@@ Line 55: / Line 56: @@
 m182_friend <- delete_edges(m182_full, E(m182_full)[E(m182_full)$friend_tie==0])
 summary(m182_friend)
+m182_friend[]
 m182_social <- delete_edges(m182_full, E(m182_full)[E(m182_full)$social_tie==0])
 summary(m182_social)
+m182_social[]
 m182_task <- delete_edges(m182_full, E(m182_full)[E(m182_full)$task_tie==0])
 summary(m182_task)
+m182_task[]
 # Look at the plots for each sub-graph
@@ Line 927: / Line 931: @@
 #####################
 </code>
+====== no pdf ======
+<code>
+##########################################################################
+# You may cite these labs as follows: McFarland, Daniel, Solomon Messing,
+# Mike Nowak, and Sean Westwood. 2010. "Social Network Analysis
+# Labs in R." Stanford University.
+##########################################################################
+##########################################################################
+# LAB 6 - Blockmodeling Lab
+# The point of this lab is to introduce students to blockmodeling
+# techniques that call for a metric of structural equivalence, a method
+# and rationale for the selection of the number of positions, and then
+# a means of summary representation (mean cutoff and reduced graph
+# presentation). Students will be shown how to identify positions using
+# correlation as a metric of structural equivalence (euclidean distance
+# is used in earlier lab), and they will be taught how to identify more
+# isomorphic notions of role-position using the triad census. Last, the
+# lab calls upon the user to compare positional techniques and come up
+# with a rationale for why they settle on one over another.
+##########################################################################
+# NOTE: if you have trouble because some packages are not installed,
+# see lab 1 for instructions on how to install all necessary packages.
+###
+#1. SETUP
+###
+library(igraph)
+library(sna)
+library(triads)
+library(psych)
+library(nFactors)
+library(NetCluster)
+###
+#2. LOADING AND FORMATTING DATA
+###
+data(studentnets.M182, package = "NetData")
+# Reduce to non-zero edges and build a graph object
+m182_full_nonzero_edges <- subset(m182_full_data_frame, (friend_tie > 0 | social_tie > 0 | task_tie > 0))
+head(m182_full_nonzero_edges)
+m182_full <- graph.data.frame(m182_full_nonzero_edges)
+summary(m182_full)
+# Create sub-graphs based on edge attributes
+m182_friend <- delete_edges(m182_full, E(m182_full)[E(m182_full)$friend_tie==0])
+summary(m182_friend)
+m182_social <- delete_edges(m182_full, E(m182_full)[E(m182_full)$social_tie==0])
+summary(m182_social)
+m182_task <- delete_edges(m182_full, E(m182_full)[E(m182_full)$task_tie==0])
+summary(m182_task)
+# Look at the plots for each sub-graph
+# pdf("6.1_m182_studentnet_friend_social_task_plots.pdf", width = 10)
+par(mfrow = c(1,3))
+friend_layout <- layout.fruchterman.reingold(m182_friend)
+plot(m182_friend, layout=friend_layout, main = "friend", edge.arrow.size=.5)
+social_layout <- layout.fruchterman.reingold(m182_social)
+plot(m182_social, layout=social_layout, main = "social", edge.arrow.size=.5)
+task_layout <- layout.fruchterman.reingold(m182_task)
+plot(m182_task, layout=task_layout, main = "task", edge.arrow.size=.5)
+# dev.off()
+###
+# 3. HIERARCHICAL CLUSTERING ON SOCIAL & TASK TIES
+###
+# We'll use the "task" and "social" sub-graphs together as the
+# basis for our structural equivalence methods. First, we'll use
+# the task graph to generate an adjacency matrix.
+#
+# This matrix represents task interactions directed FROM the
+# row individual TO the column individual.
+m182_task_matrix_row_to_col <- get.adjacency(m182_task, attr='task_tie')
+m182_task_matrix_row_to_col
+# To operate on a binary graph, simply leave off the "attr"
+# parameter:
+m182_task_matrix_row_to_col_bin <- get.adjacency(m182_task)
+m182_task_matrix_row_to_col_bin
+# For this lab, we'll use the valued graph. The next step is to
+# concatenate it with its transpose in order to capture both
+# incoming and outgoing task interactions.
+m182_task_matrix_col_to_row <- t(as.matrix(m182_task_matrix_row_to_col))
+m182_task_matrix_col_to_row
+m182_task_matrix <- rbind(m182_task_matrix_row_to_col, m182_task_matrix_col_to_row)
+m182_task_matrix
+# Next, we'll use the same procedure to add social-interaction
+# information.
+m182_social_matrix_row_to_col <- get.adjacency(m182_social, attr='social_tie')
+m182_social_matrix_row_to_col
+m182_social_matrix_row_to_col_bin <- get.adjacency(m182_social)
+m182_social_matrix_row_to_col_bin
+m182_social_matrix_col_to_row <- t(as.matrix(m182_social_matrix_row_to_col))
+m182_social_matrix_col_to_row
+m182_social_matrix <- rbind(m182_social_matrix_row_to_col, m182_social_matrix_col_to_row)
+m182_social_matrix
+m182_task_social_matrix <- rbind(m182_task_matrix, m182_social_matrix)
+m182_task_social_matrix
+# Now we have a single 4n x n matrix that represents both in- and
+# out-directed task and social communication. From this, we can
+# generate an n x n correlation matrix that shows the degree of
+# structural equivalence of each actor in the network.
+m182_task_social_cors <- cor(as.matrix(m182_task_social_matrix))
+m182_task_social_cors
+# To use correlation values in hierarchical NetCluster, they must
+# first be coerced into a "dissimilarity structure" using dist().
+# We subtract the values from 1 so that they are all greater than
+# or equal to 0; thus, highly dissimilar (i.e., negatively
+# correlated) actors have higher values.
+dissimilarity <- 1 - m182_task_social_cors
+m182_task_social_dist <- as.dist(dissimilarity)
+m182_task_social_dist
+# Note that it is also possible to use dist() directly on the
+# matrix. However, since cor() looks at associations between
+# columns and dist() looks at associations between rows, it is
+# necessary to transpose the matrix first.
+#
+# A variety of distance metrics are available; Euclidean
+# is the default.
+#m182_task_social_dist <- dist(t(m182_task_social_matrix))
+#m182_task_social_dist
+# hclust() performs a hierarchical agglomerative NetCluster
+# operation based on the values in the dissimilarity matrix
+# yielded by as.dist() above. The standard visualization is a
+# dendrogram. By default, hclust() agglomerates clusters via a
+# "complete linkakage" algorithm, determining cluster proximity
+# by looking at the distance of the two points across clusters
+# that are farthest away from one another. This can be changed via
+# the "method" parameter.
+# pdf("6.2_m182_studentnet_social_hclust.pdf")
+m182_task_social_hclust <- hclust(m182_task_social_dist)
+plot(m182_task_social_hclust)
+# dev.off()
+# cutree() allows us to use the output of hclust() to set
+# different numbers of clusters and assign vertices to clusters
+# as appropriate. For example:
+cutree(m182_task_social_hclust, k=2)
+# Now we'll try to figure out the number of clusters that best
+# describes the underlying data. To do this, we'll loop through
+# all of the possible numbers of clusters (1 through n, where n is
+# the number of actors in the network). For each solution
+# corresponding to a given number of clusters, we'll use cutree()
+# to assign the vertices to their respective clusters
+# corresponding to that solution.
+#
+# From this, we can generate a matrix of within- and between-
+# cluster correlations. Thus, when there is one cluster for each
+# vertex in the network, the cell values will be identical to the
+# observed correlation matrix, and when there is one cluster for
+# the whole network, the values will all be equal to the average
+# correlation across the observed matrix.
+#
+# We can then correlate each by-cluster matrix with the observed
+# correlation matrix to see how well the by-cluster matrix fits
+# the data. We'll store the correlation for each number of
+# clusters in a vector, which we can then plot.
+# First, we initialize a vector for storing the correlations and
+# set a variable for our number of vertices.
+clustered_observed_cors = vector()
+num_vertices = length(V(m182_task))
+# Next, we loop through the different possible cluster
+# configurations, produce matrices of within- and between-
+# cluster correlations, and correlate these by-cluster matrices
+# with the observed correlation matrix.
+# pdf("6.3_m182_studentnet_task_social_clustered_observed_corrs.pdf")
+clustered_observed_cors <-clustConfigurations(num_vertices,m182_task_social_hclust,m182_task_social_cors)
+clustered_observed_cors
+plot(clustered_observed_cors$correlations)
+# dev.off()
+clustered_observed_cors$correlations
+# From a visual inspection of the correlation matrix, we can
+# decide on the proper number of clusters in this network.
+# For this network, we'll use 4. (Note that the 1-cluster
+# solution doesn't appear on the plot because its correlation
+# with the observed correlation matrix is undefined.)
+num_clusters = 4
+clusters <- cutree(m182_task_social_hclust, k = num_clusters)
+clusters
+cluster_cor_mat <- clusterCorr(m182_task_social_cors,
+                                            clusters)
+cluster_cor_mat
+# Let's look at the correlation between this cluster configuration
+# and the observed correlation matrix. This should match the
+# corresponding value from clustered_observed_cors above.
+gcor(cluster_cor_mat, m182_task_social_cors)
+#####################
+# Questions:
+# (1) What rationale do you have for selecting the number of
+# clusters / positions that you do?
+#####################
+### NOTE ON DEDUCTIVE CLUSTERING
+# It's pretty straightforward, using the code above, to explore
+# your own deductive NetCluster. Simply supply your own cluster
+# vector, where the elements in the vector are in the same order
+# as the vertices in the matrix, and the values represent the
+# cluster to which each vertex belongs.
+#
+# For example, if you believed that actors 2, 7, and 8 formed one
+# group, actor 16 former another group, and everyone else formed
+# a third group, you could represent this as follows:
+deductive_clusters = c(1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1,
+, 3)
+# You could then examine the fitness of this cluster configuration
+# as follows:
+deductive_cluster_cor_mat <- generate_cluster_cor_mat(
+  m182_task_social_cors,
+  deductive_clusters)
+deductive_cluster_cor_mat
+gcor(deductive_cluster_cor_mat, m182_task_social_cors)
+### END NOTE ON DEDUCTIVE CLUSTERING
+# Now we'll use the 4-cluster solution to generate blockmodels,
+# using the raw tie data from the underlying task and social
+# networks.
+# Task valued
+task_mean <- mean(as.matrix(m182_task_matrix_row_to_col))
+task_mean
+task_valued_blockmodel <- blockmodel(as.matrix(m182_task_matrix_row_to_col), clusters)
+task_valued_blockmodel
+# Task binary
+task_density <- graph.density(m182_task)
+task_density
+task_binary_blockmodel <- blockmodel(as.matrix(m182_task_matrix_row_to_col_bin), clusters)
+task_binary_blockmodel
+# Social valued
+social_mean <- mean(as.matrix(m182_social_matrix_row_to_col))
+social_mean
+social_valued_blockmodel <- blockmodel(as.matrix(m182_social_matrix_row_to_col), clusters)
+social_valued_blockmodel
+# Social binary
+social_density <- graph.density(m182_social)
+social_density
+social_binary_blockmodel <- blockmodel(as.matrix(m182_social_matrix_row_to_col_bin), clusters)
+social_binary_blockmodel
+# We can also permute the network to examine the within- and
+# between-cluster correlations.
+cluster_cor_mat_per <- permute_matrix(clusters, cluster_cor_mat)
+cluster_cor_mat_per
+#####################
+# Questions:
+# (2) What is the story you get from viewing these clusters,
+# and their within and between cluster densities on task and
+# social interaction? What can you say about M182 from this?
+#####################
+#
+# 4. deleted.
+#
+#####################
+# Questions:
+# (3) What does clustering of the triadic census afford us?
+# What roles do you see? Redo the initial blockmodel analysis
+# without social interaction (only task) and then compare to
+# this solution. Do they differ?
+#
+# Extra credit: Try running the triad census on task AND
+# social interaction separately and then correlating persons.
+# What result do you get? Is it different from our initial
+# blockmodel result? Show your code.
+######################
+###
+# 5. FACTOR ANALYSIS
+###
+# Note that although we are conducting a principal components
+# analysis (PCA), which is technically not exactly the same as
+# factor analysis, we will use the term "factor" to describe the
+# individual components in our PCA.
+# PCA is often used in network analysis as a form of detecting
+# individuals global positioning. We say "global" because these
+# clusters aren't defined on local cohesion but from the overall
+# pattern of ties individuals have with all others (structural
+# equivalence). Identifying the first two largest components that
+# organize the variance in tie patterns is one way of doing this.
+# We'll analyze the 4n x n matrix generated above.
+# First, we want to determine the ideal number of components
+# (factors) to extract. We'll do this by examining the eigenvalues
+# in a scree plot and examining how each number of factors stacks
+# up to a few proposed non-graphical solutions to selecting the
+# optimal number of components, available via the nFactors
+# package.
+ev <- eigen(cor(as.matrix(m182_task_social_matrix))) # get eigenvalues
+ap <- parallel(subject=nrow(m182_task_social_matrix),
+		var=ncol(m182_task_social_matrix),
+		rep=100,cent=.05)
+nS <- nScree(ev$values, ap$eigen$qevpea)
+# pdf("6.6_m182_studentnet_task_social_pca_scree.pdf")
+plotnScree(nS)
+# To draw a line across the graph where eigenvalues are = 1,
+# use the following code:
+plotnScree(nS)
+abline(h=1)
+# dev.off()
+# For more information on this procedure, please see
+# the references provided in the parallel() documentation
+# (type "?parallel" in the R command line with the package
+# loaded).
+# Now we'll run a principal components analysis on the matrix,
+# using the number of factors determined above (note this may not
+# be the same number as you get):
+pca_m182_task_social = principal(as.matrix(m182_task_social_matrix), nfactors=5, rotate="varimax")
+# Let's take a look at the results in the R terminal:
+pca_m182_task_social
+# You can see the standardized loadings for each factor for each
+# node. Note that R sometimes puts the factors in a funky order
+# (e.g. RC1, RC2, RC5, RC4, RC3) but all of the factors are there.
+# You can see that the SS loadings, proportion of variance
+# explained and cumulative variance explained is provided below. A
+# Chi Square test of the factors and various other statistics are
+# provided below.
+# Note that the eigenvalues can be accessed via the following
+# command:
+pca_m182_task_social$values
+# Now we will use the factor loadings to cluster and compare that
+# to our other NetCluster techniques, using dendrograms.
+# Take the distance based on Euclidian Distance
+m182_task_factor_dist = dist(pca_m182_task_social$loadings)
+# And cluster
+m182_task_factor_hclust <- hclust(m182_task_factor_dist)
+# pdf("6.7_m182_studentnet_task_social_pca_hclust.pdf")
+plot(m182_task_factor_hclust)
+# dev.off()
+# And compare to NetCluster based on correlations and triads:
+# pdf("6.8_m182_task_cluster_by_correlation_PCA_Triads.pdf")
+par(mfrow = c(1,3))
+plot(m182_task_social_hclust, main = "Correlation")
+plot(m182_task_factor_hclust, main = "PCA")
+plot(m182_task_triad_hclust, main = "Triads")
+# dev.off()
+#####################
+# Questions:
+# (4) How do the results across blockmodel techniques differ?
+# Why might you use one over the other? Why might you want to
+# run more than one in your analyses?
+#####################
+</code>