#Created September 25, 2009
#modified November 28, 2009 to allow top down as well as left right (default)
#based upon structure graph but not using Rgraphviz
#creates a structural equation path diagram, draws it, and saves sem commands
#modified again in December, 2009 to add Rx, Ry options
"structure.diagram" <-
function(fx=NULL,Phi=NULL,fy=NULL,labels=NULL,cut=.3,errors=FALSE,simple=TRUE,regression=FALSE,lr=TRUE,Rx=NULL,Ry=NULL,
digits=1,e.size=.1,main="Structural model", ...){
#first some default values
xmodel <- fx
ymodel <- fy
num.y <- num.x <- 0 #we assume there is nothing there
if(!is.null(fx) ) { #this is the normal case
#check if input is from a factor analysis or omega analysis
if(!is.null(class(xmodel)) && (length(class(xmodel))>1)) {
if(class(xmodel)[1] =="psych" && class(xmodel)[2] =="omega") {
Phi <- xmodel$schmid$phi
xmodel <- xmodel$schmid$oblique} else {
if(class(xmodel)[1] =="psych" && ((class(xmodel)[2] =="fa") | (class(xmodel)[2] =="principal"))) { if(!is.null(xmodel$Phi)) Phi <- xmodel$Phi
xmodel <- as.matrix(xmodel$loadings)}
}} else {
if(!is.matrix(xmodel) & !is.data.frame(xmodel) &!is.vector(xmodel)) {
if(!is.null(xmodel$Phi)) Phi <- xmodel$Phi
xmodel <- as.matrix(xmodel$loadings)
} else {xmodel <- xmodel}
}
#first some basic setup parameters -- these just convert the various types of input
if(!is.matrix(xmodel) ) {factors <- as.matrix(xmodel)} else {factors <- xmodel}
num.var <- num.xvar <- dim(factors)[1] #how many x variables?
if (is.null(num.xvar) ){num.xvar <- length(factors)
num.xfactors <- 1} else {
num.factors <- num.xfactors <- dim(factors)[2]}
if(is.null(labels)) {vars <- xvars <- rownames(xmodel)} else { xvars <- vars <- labels}
if(is.null(vars) ) {vars <- xvars <- paste("x",1:num.xvar,sep="") }
fact <- colnames(xmodel)
if (is.null(fact)) { fact <- paste("X",1:num.xfactors,sep="") }
if(is.numeric(factors)) {factors <- round(factors,digits) }
} else {#fx is NULL This is for the case where we want to do some fancy graphics of sems
num.xvar <- dim(Rx)[1]
num.xfactors <- 0
num.yfactors <- 0
num.factors <- 0
if(is.null(labels)) {vars <- xvars <- rownames(Rx)} else { xvars <- vars <- labels}
}
num.yfactors <- 0
num.yvar <- 0
if (!is.null(ymodel)) {
if(is.list(ymodel) & !is.data.frame(ymodel) ) {ymodel <- as.matrix(ymodel$loadings)} else {ymodel <- ymodel}
if(!is.matrix(ymodel) ) {y.factors <- as.matrix(ymodel)} else {y.factors <- ymodel}
num.y <- dim(y.factors)[1]
if (is.null(num.y)) {
num.y <- length(ymodel)
num.yfactors <- 1} else {
num.yfactors <- dim(y.factors)[2]
}
num.yvar <- num.y
yvars <- rownames(ymodel)
if(is.null(yvars)) {yvars <- paste("y",1:num.y,sep="") }
if(is.null(labels)) {vars <- c(xvars,yvars)} else {yvars <- labels[(num.xvar+1):(num.xvar+num.y)]}
yfact <- colnames(ymodel)
if(is.null(yfact)) {yfact <- paste("Y",1:num.yfactors,sep="") }
fact <- c(fact,yfact)
if(is.numeric(y.factors)) {y.factors <- round(y.factors,digits)
}
}#end of if(null(y.model))
if(!is.null(Ry)& is.null(ymodel)) {num.yvar <- num.y <- dim(Ry)[1]
yvars <- colnames(Ry)} #do we want to draw the inter Y correlations?
num.var <- num.xvar + num.y
num.factors <- num.xfactors + num.yfactors
sem <- matrix(rep(NA),6*(num.var*num.factors + num.factors),ncol=3) #this creates an output model for sem analysis
lavaan <- vector("list",num.xfactors + num.yfactors) #create a list for lavaan
colnames(sem) <- c("Path","Parameter","Value")
var.rect <- list()
fact.rect <- list()
if(is.numeric(Phi) ) { Phi <- round(Phi,digits)}
if(!is.null(Rx)) {x.curves <- 2
if(is.numeric(Rx) ) { Rx <- round(Rx,digits)}} else {x.curves <- 0 }
if(!is.null(Ry)) {y.curves <- 3
if(is.numeric(Ry) ) { Ry <- round(Ry,digits)}} else {y.curves <- 0}
###create the basic figure
length.labels <- 0 # a filler for now
#plot.new() is necessary if we have not plotted before
#strwd <- try(strwidth(xvars),silent=TRUE)
strwd <- try(length.labels <- max(strwidth(xvars),strwidth("abc"))/1.8,silent=TRUE) #although this throws an error if the window is not already open, we don't show it
#if (class(strwd) == "try-error" ) {plot.new() }
if (class(strwd) == "try-error" ) {length.labels = max(nchar(xvars),3)/1.8 }
#length.labels <- max(strwidth(xvars),strwidth("abc"))/1.8
if(lr) {limx <- c(-(length.labels+ x.curves),max(num.xvar,num.yvar)+2 + y.curves)
limy <- c(0,max(num.xvar,num.yvar)+1) } else {
limy <- c(-(length.labels+x.curves),max(num.xvar,num.yvar) +2 + y.curves)
limx <- c(0,max(num.xvar,num.yvar)+1)
if( errors) limy <- c(-1,max(num.xvar,num.yvar)+2)}
scale.xaxis <- 3
if(lr) {plot(0,type="n",xlim=limx,ylim=limy,frame.plot=FALSE,axes=FALSE,ylab="",xlab="",main=main)} else {plot(0,type="n",xlim=limx,ylim=limy,frame.plot=FALSE,axes=FALSE,ylab="",xlab="",main=main) }
#now draw the x part
k <- num.factors
for (v in 1:num.xvar) {
if(lr) { var.rect[[v]] <- dia.rect(0,num.xvar-v+1,xvars[v],xlim=limx,ylim=limy,...) } else { var.rect[[v]] <- dia.rect(v,0,xvars[v],xlim=limy,ylim=limx,...) }
}
nvar <- num.xvar
f.scale <- (num.xvar+ 1)/(num.xfactors+1)
if (num.xfactors >0) {
for (f in 1:num.xfactors) {
if(!regression) {if(lr) {fact.rect[[f]] <- dia.ellipse(limx[2]/scale.xaxis,(num.xfactors+1-f)*f.scale,fact[f],xlim=c(0,nvar),ylim=c(0,nvar),e.size=e.size,...)} else {fact.rect[[f]] <- dia.ellipse(f*f.scale,limy[2]/scale.xaxis,fact[f],ylim=c(0,nvar),xlim=c(0,nvar),e.size=e.size,...)
}
} else {if(lr) {fact.rect[[f]] <- dia.rect(limx[2]/scale.xaxis,(num.xfactors+1-f)*f.scale,fact[f],xlim=c(0,nvar),ylim=c(0,nvar),...)} else {
fact.rect[[f]] <- dia.rect(f*f.scale,limy[2]/scale.xaxis,fact[f],xlim=c(0,nvar),ylim=c(0,nvar),...)}
}
for (v in 1:num.xvar) {
if(is.numeric(factors[v,f])) {
if(simple && (abs(factors[v,f]) == max(abs(factors[v,])) ) && (abs(factors[v,f]) > cut) | (!simple && (abs(factors[v,f]) > cut))) { if (!regression) {if(lr){dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$right,labels =factors[v,f],col=((sign(factors[v,f])<0) +1),lty=((sign(factors[v,f])<0) +1))
} else {dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$top,labels =factors[v,f],col=((sign(factors[v,f])<0) +1),lty=((sign(factors[v,f])<0) +1))
}
} else {dia.arrow(to=fact.rect[[f]]$left,from=var.rect[[v]]$right,labels =factors[v,f],col=((sign(factors[v,f])<0) +1))} }
} else {
if (factors[v,f] !="0") {
if (!regression) { if(lr) {dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$right,labels =factors[v,f]) } else {dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$top,labels =factors[v,f])}
} else {if(lr) {dia.arrow(to=fact.rect[[f]],from=var.rect[[v]]$right,labels =factors[v,f])} else {dia.arrow(to=fact.rect[[f]],from=var.rect[[v]]$top,labels =factors[v,f])}
} }
} }
}
if (num.xfactors ==1) {
lavaan[[1]] <- paste(fact[1],"=~ ")
for(i in 1:num.xvar) {
sem[i,1] <- paste(fact[1],"->",vars[i],sep="")
lavaan[[1]] <- paste0(lavaan[[1]], ' + ', vars[i])
if(is.numeric(factors[i])) {sem[i,2] <- vars[i]} else {sem[i,2] <- factors[i] }
}} #end of if num.xfactors ==1
k <- num.xvar+1
k <- 1
for (f in 1:num.xfactors) { #if (!is.numeric(factors[i,f]) || (abs(factors[i,f]) > cut))
lavaan[[f]] <- paste0(fact[f] ," =~ ")
for (i in 1:num.xvar) {
if((!is.numeric(factors[i,f] ) && (factors[i,f] !="0"))|| ((is.numeric(factors[i,f]) && abs(factors[i,f]) > cut ))) {
sem[k,1] <- paste(fact[f],"->",vars[i],sep="")
lavaan[[f]] <- paste0(lavaan[[f]], ' + ', vars[i])
if(is.numeric(factors[i,f])) {sem[k,2] <- paste("F",f,vars[i],sep="")} else {sem[k,2] <- factors[i,f]}
k <- k+1 } #end of if
}
}
} #end of if num.xfactors > 0
if(errors) { for (i in 1:num.xvar) {if(lr) { dia.self(var.rect[[i]],side=2) } else { dia.self(var.rect[[i]],side=1)}
sem[k,1] <- paste(vars[i],"<->",vars[i],sep="")
sem[k,2] <- paste("x",i,"e",sep="")
k <- k+1 }
}
#now, if there is a ymodel, do it for y model
if(!is.null(ymodel)| !is.null(Ry)) {
if(lr) { y.adj <- num.yvar/2 - num.xvar/2
f.yscale <- limy[2]/(num.yfactors+1)
y.fadj <- 0} else {
y.adj <- num.xvar/2 - num.yvar/2
f.yscale <- limx[2]/(num.yfactors+1)
y.fadj <- 0}
for (v in 1:num.yvar) { if(lr){ var.rect[[v+num.xvar]] <- dia.rect(limx[2]-y.curves,limy[2]-v + y.adj,yvars[v],xlim=limx,ylim=limy,...)} else {
var.rect[[v+num.xvar]] <- dia.rect(v + y.adj,limx[2],yvars[v],xlim=limy,ylim=limx,...)}
}
}
#we have drawn the y variables, now should we draw the Y factors
if(!is.null(ymodel)){
for (f in 1:num.yfactors) {if(lr) {
fact.rect[[f+num.xfactors]] <- dia.ellipse(2*limx[2]/scale.xaxis,(num.yfactors+1-f)*f.yscale +y.fadj,yfact[f],xlim=c(0,nvar),ylim=c(0,nvar),e.size=e.size,...)} else {
fact.rect[[f+num.xfactors]] <- dia.ellipse(f*f.yscale+ y.fadj,2*limx[2]/scale.xaxis,yfact[f],ylim=c(0,nvar),xlim=c(0,nvar),e.size=e.size,...)}
for (v in 1:num.yvar) {if(is.numeric(y.factors[v,f])) {
{if(simple && (abs(y.factors[v,f]) == max(abs(y.factors[v,])) ) && (abs(y.factors[v,f]) > cut) | (!simple && (abs(factors[v,f]) > cut))) {
if(lr) { dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$left,labels =y.factors[v,f],col=((sign(y.factors[v,f])<0) +1))} else {
dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$bottom,labels =y.factors[v,f],col=((sign(y.factors[v,f])<0) +1))}
}
}
} else {if(factors[v,f] !="0") {if(lr) {dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$left,labels =y.factors[v,f]) } else {
dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$bottom,labels =y.factors[v,f])
}
}
}}
}
if (num.yfactors ==1) {
for (i in 1:num.y) { sem[k,1] <- paste(fact[1+num.xfactors],"->",yvars[i],sep="")
if(is.numeric(y.factors[i] ) ) {sem[k,2] <- paste("Fy",yvars[i],sep="")} else {sem[k,2] <- y.factors[i]}
k <- k +1
}
} else { #end of if num.yfactors ==1
for (i in 1:num.y) {
for (f in 1:num.yfactors) {
if( (y.factors[i,f] !="0") && (abs(y.factors[i,f]) > cut )) {
sem[k,1] <- paste(fact[f+num.xfactors],"->",vars[i+num.xvar],sep="")
if(is.numeric(y.factors[i,f])) { sem[k,2] <- paste("Fy",f,vars[i+num.xvar],sep="")} else {sem[k,2] <- y.factors[i,f]}
k <- k+1 } #end of if
} #end of factor
} # end of variable loop
} #end of else if
# }
if(errors) { for (i in 1:num.y) {
if(lr) {dia.self(var.rect[[i+num.xvar]],side=3) } else {dia.self(var.rect[[i+num.xvar]],side=3)}
sem[k,1] <- paste(vars[i+num.xvar],"<->",vars[i+num.xvar],sep="")
sem[k,2] <- paste("y",i,"e",sep="")
k <- k+1 }}
} #end of if.null(ymodel)
if(!is.null(Rx)) {#draw the correlations between the x variables
for (i in 2:num.xvar) {
for (j in 1:(i-1)) {
if((!is.numeric(Rx[i,j] ) && ((Rx[i,j] !="0")||(Rx[j,i] !="0")))|| ((is.numeric(Rx[i,j]) && abs(Rx[i,j]) > cut ))) {
if (lr) {if(abs(i-j) < 2) { dia.curve(from=var.rect[[j]]$left,to=var.rect[[i]]$left, labels = Rx[i,j],scale=-3*(i-j)/num.xvar)} else { dia.curve(from=var.rect[[j]]$left,to=var.rect[[i]]$left, labels = Rx[i,j],scale=-3*(i-j)/num.xvar)}
} else {
if(abs(i-j) < 2) { dia.curve(from=var.rect[[j]]$bottom,to=var.rect[[i]]$bottom, labels = Rx[i,j],scale=-3*(i-j)/num.xvar)} else {dia.curve(from=var.rect[[j]]$bottom,to=var.rect[[i]]$bottom, labels = Rx[i,j],scale=-3*(i-j)/num.xvar)}
}
}}
}
}
if(!is.null(Ry)) {#draw the correlations between the y variables
for (i in 2:num.yvar) {
for (j in 1:(i-1)) {
if((!is.numeric(Ry[i,j] ) && ((Ry[i,j] !="0")||(Ry[j,i] !="0")))|| ((is.numeric(Ry[i,j]) && abs(Ry[i,j]) > cut ))) {
if (lr) {if(abs(i-j) < 2) { dia.curve(from=var.rect[[j+num.xvar]]$right,to=var.rect[[i+num.xvar]]$right, labels = Ry[i,j],scale=3*(i-j)/num.xvar)} else {dia.curve(from=var.rect[[j+num.xvar]]$right,to=var.rect[[i+num.xvar]]$right, labels = Ry[i,j],scale=3*(i-j)/num.xvar)}
} else {
if(abs(i-j) < 2) { dia.curve(from=var.rect[[j+num.xvar]]$bottom,to=var.rect[[i+num.xvar]]$bottom, labels = Ry[i,j],scale=3*(i-j)/num.xvar)} else {dia.curve(from=var.rect[[j+num.xvar]]$bottom,to=var.rect[[i+num.xvar]]$bottom, labels = Ry[i,j],scale=3*(i-j)/num.xvar)}
}
}}
}
}
if(!regression) {
if(!is.null(Phi)) {if (!is.matrix(Phi)) { if(!is.null(fy)) {Phi <- matrix(c(1,0,Phi,1),ncol=2)} else {Phi <- matrix(c(1,Phi,Phi,1),ncol=2)}}
if(num.xfactors>1) {for (i in 2:num.xfactors) { #first do the correlations within the f set
for (j in 1:(i-1)) {
{if((!is.numeric(Phi[i,j] ) && ((Phi[i,j] !="0")||(Phi[j,i] !="0")))|| ((is.numeric(Phi[i,j]) && abs(Phi[i,j]) > cut ))) {
if(Phi[i,j] == Phi[j,i] ) {
if(lr) {dia.curve(from=fact.rect[[i]]$right,to=fact.rect[[j]]$right, labels = Phi[i,j],scale=2*(i-j)/num.xfactors)} else {
dia.curve(from=fact.rect[[i]]$top,to=fact.rect[[j]]$top, labels = Phi[i,j],scale=2*(i-j)/num.xfactors)}
sem[k,1] <- paste(fact[i],"<->",fact[j],sep="")
sem[k,2] <- paste("rF",i,"F",j,sep="")} else {#directed arrows
if(Phi[i,j] !="0") { if(lr) { if(abs(i-j) < 2) {dia.arrow(from=fact.rect[[j]],to=fact.rect[[i]], labels = Phi[i,j],scale=2*(i-j)/num.xfactors)} else {
dia.curved.arrow(from=fact.rect[[j]]$right,to=fact.rect[[i]]$right, labels = Phi[i,j],scale=2*(i-j)/num.xfactors)}
} else {
if(abs(i-j) < 2) { dia.arrow(from=fact.rect[[j]],to=fact.rect[[i]], labels = Phi[i,j],scale=2*(i-j)/num.xfactors)} else {
dia.curved.arrow(from=fact.rect[[j]]$top,to=fact.rect[[i]]$top, labels = Phi[i,j],scale=2*(i-j)/num.xfactors)}
}
sem[k,1] <- paste(fact[j]," ->",fact[i],sep="")
sem[k,2] <- paste("rF",j,"F",i,sep="")} else {
if(lr) { if(abs(i-j) < 2) {dia.arrow(from=fact.rect[[i]],to=fact.rect[[j]], labels = Phi[j,i],scale=2*(i-j)/num.xfactors)} else {
dia.curved.arrow(from=fact.rect[[i]]$right,to=fact.rect[[j]]$right, labels = Phi[j,i],scale=2*(i-j)/num.xfactors)}
} else {
if(abs(i-j) < 2) { dia.arrow(from=fact.rect[[i]],to=fact.rect[[j]], labels = Phi[j,i],scale=2*(i-j)/num.xfactors)} else {
dia.curved.arrow(from=fact.rect[[i]]$top,to=fact.rect[[j]]$top, labels = Phi[j,i],scale=2*(i-j)/num.xfactors)}
}
sem[k,1] <- paste(fact[i],"<-",fact[j],sep="")
sem[k,2] <- paste("rF",i,"F",j,sep="")}
} } else {
sem[k,1] <- paste(fact[i],"<->",fact[j],sep="")
if (is.numeric(Phi[i,j])) {sem[k,2] <- paste("rF",i,"F",j,sep="")} else {sem[k,2] <- Phi[i,j] } }
k <- k + 1} }
}
} #end of correlations within the fx set
if(!is.null(ymodel)) {
for (i in 1:num.xfactors) {
for (j in 1:num.yfactors) {
if((!is.numeric(Phi[j+num.xfactors,i] ) && (Phi[j+num.xfactors,i] !="0"))|| ((is.numeric(Phi[j+num.xfactors,i]) && abs(Phi[j+num.xfactors,i]) > cut ))) {
dia.arrow(from=fact.rect[[i]],to=fact.rect[[j+num.xfactors]],Phi[j+num.xfactors,i])
sem[k,1] <- paste(fact[i],"->",fact[j+num.xfactors],sep="") } else {
sem[k,1] <- paste(fact[i],"<->",fact[j+num.xfactors],sep="")}
if (is.numeric(Phi[j+num.xfactors,i])) {sem[k,2] <- paste("rX",i,"Y",j,sep="")} else {sem[k,2] <- Phi[j+num.xfactors,i] }
k <- k + 1 }
} }
} }
if(num.factors > 0 ) {
for(f in 1:num.factors) {
sem[k,1] <- paste(fact[f],"<->",fact[f],sep="")
sem[k,3] <- "1"
k <- k+1
}
model=sem[1:(k-1),]
class(model) <- "mod" #suggested by John Fox to make the output cleaner
lavaan <- unlist(lavaan)
lavaan <- noquote(lavaan)
result <- list(sem=model,lavaan=lavaan)
return(invisible(result)) }
}
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