fa.graph: Graph factor loading matrices

Description

Factor analysis or principal components analysis results are typically interpreted in terms of the major loadings on each factor. These structures may be represented as a table of loadings or graphically, where all loadings with an absolute value > some cut point are represented as an edge (path).

Usage

fa.graph(fa.results, out.file = NULL, labels = NULL, cut = 0.3, simple = TRUE, size = c(8, 6), node.font = c("Helvetica", 14), edge.font = c("Helvetica", 10), rank.direction = "RL", digits = 1, title = "Factor Analysis", ...)

Arguments

fa.results

The output of factor analysis or principal components analysis

out.file

If it exists, a dot representation of the graph will be stored here

labels

Variable labels

cut

Loadings with abs(loading) > cut will be shown

simple

Only the biggest loading per item is shown

size

node.font

edge.font

rank.direction

digits

Number of digits to show as an edgelable

title

Graphic title

...

other parameters

Value

A graph is drawn using rgraphviz. If an output file is specified, the graph instructions are also saved in the dot language.

Details

Path diagram representations have become standard in confirmatory factor analysis, but are not yet common in exploratory factor analysis. Representing factor structures graphically helps some people understand the structure.

Examples

Run this code

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.
# test.simple <- factor.pa(item.sim(16),2)
#fa.graph(test.simple)

## The function is currently defined as
function(fa.results,out.file=NULL,labels=NULL,cut=.3,simple=TRUE,
   size=c(8,6), node.font=c("Helvetica", 14),
    edge.font=c("Helvetica", 10), rank.direction="RL", digits=1,title="Factor Analysis", ...){
    require(Rgraphviz)
    
factors <- as.matrix(fa.results$loadings)
   rank.direction <- match.arg(rank.direction)
  #first some basic setup parameters 
  
   num.var <- dim(factors)[1]   #how many variables?
   if (is.null(num.var) ){num.var <- length(factors)
       num.factors <- 1} else {
   num.factors <- dim(factors)[2]}
   if (simple) {k=1} else {k <- num.factors}
   vars <- paste("V",1:num.var,sep="")   
   fact <- paste("F",1:num.factors,sep="")
   clust.graph <-  new("graphNEL",nodes=c(vars,fact),edgemode="directed")
   graph.shape <- c(rep("box",num.var),rep("ellipse",num.factors))
   graph.rank <- c(rep("sink",num.var),rep("",num.factors))
   names(graph.shape) <- nodes(clust.graph)
   names(graph.rank) <- nodes(clust.graph)
   edge.label <- rep("",num.var*k)
   edge.name <- rep("",num.var*k)
   names(edge.label) <-  seq(1:num.var*k) 
            
  #show the cluster structure with ellipses

  l <- factors 
  if (num.factors ==1) { 
       
    for (i in 1:num.var) { clust.graph <- addEdge(fact[1], vars[i], clust.graph,1) 
                         edge.label[i] <- round(factors[i],digits)
                         edge.name[i] <- paste(fact[1],"~",vars[i],sep="")
                        }  
      } else { 
     if(simple){   #very simple structure is one loading per variable
        m1 <- matrix(apply(t(apply(l, 1, abs)), 1, which.max), 
        ncol = 1)       
        for (i in 1:num.var) {clust.graph <- addEdge(fact[m1[i]], vars[i], clust.graph,1) 
                         edge.label[i] <- round(factors[i,m1[i]],digits)
                         edge.name[i] <- paste(fact[m1[i]],"~",vars[i],sep="")
                        }  
                  }   else {   #all loadings > cut in absolute value
                   k <- 1
                   for (i in 1:num.var) {
                   for (f in 1:num.factors) { if (abs(factors[i,f]) > cut) {clust.graph <- addEdge(fact[f], vars[i], clust.graph,1) 
                         edge.label[k] <- round(factors[i,f],digits)
                         edge.name[k] <- paste(fact[f],"~",vars[i],sep="")
                         k <- k+1 }   #end of if 
                         }  #end of factor
                        } # end of variable loop
            }  #end of if simple else
       }   #end of if num.factors ==1 
                  
 nAttrs <- list()  #node attributes
 eAttrs <- list()  #edge attributes


 if (!is.null(labels)) {var.labels <- c(labels,fact)
  names(var.labels) <-  nodes(clust.graph)
  nAttrs$label <- var.labels
  names(edge.label) <- edge.name
  } 
    names(edge.label) <- edge.name
 nAttrs$shape <- graph.shape
 nAttrs$rank <- graph.rank
 eAttrs$label <- edge.label
 attrs <- list(node = list(shape = "ellipse", fixedsize = FALSE),graph=list(rankdir=rank.direction, fontsize=10,bgcolor="white" ))
 obs.var <- subGraph(vars,clust.graph)
 cluster.vars <- subGraph(fact,clust.graph)
 observed <- list(list(graph=obs.var,cluster=TRUE,attrs=c(rank="")))
 plot(clust.graph, nodeAttrs = nAttrs, edgeAttrs = eAttrs, attrs = attrs,subGList=observed) 
if(!is.null(out.file) ){toDot(clust.graph,out.file,nodeAttrs = nAttrs, edgeAttrs = eAttrs, attrs = attrs) }
return(clust.graph)
   }