R/structure.diagram.R

In psych: Procedures for Psychological, Psychometric, and Personality Research

#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
#modified to produce correct sem and lavaan code  October 2018
#modified 11/14/18 to do mimic models

"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 
  e.size <- e.size*8/(NROW(fx))
 #check if input is from a factor analysis or omega analysis
 if(!is.null(class(xmodel)) && (length(class(xmodel))>1)) {
   if((inherits(xmodel,"psych") && inherits(xmodel, "omega"))) {
    Phi <- xmodel$schmid$phi
    xmodel <- xmodel$schmid$oblique} else {
   if((inherits(xmodel,"psych") && ((inherits(xmodel,"fa") | (inherits(xmodel,"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]
     if(is.null(num.xvar)) num.xvar <- 0
     num.xfactors <- 0
     num.yfactors <- 0
     num.factors <- 0
     fact <- NULL

      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
    if((num.xfactors > 0 ) & (num.yfactors > 0) & is.null(Phi)) {mimic <- TRUE
    num.factors <- max(num.xfactors,num.yfactors)} else {mimic <- FALSE
    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}



## now do the basic scaling of the figure 
###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 (inherits(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+ errors/4),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+errors)  
      limx <-  c(0,max(num.xvar,num.yvar)+1)    
     # if( errors)   limy <- c(-1,max(num.xvar,num.yvar)+2)
       }
scale.xaxis <- 3
#max(num.xvar +1,num.yvar+1)/(num.xfactors+1)

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
#we want to center the x factors on the left side
#this requires adding an adjustment if there are more y variables than x  variables.
#do not draw any x variable if fx is not specified
 x.adj <- max(0,num.yvar - num.xvar)/2  
 k <- num.factors  
 x.scale <- max(num.xvar +1,num.yvar+1)/(num.xvar+1)

if(num.xvar > 0)   { #the normal case 
    for (v in 1:num.xvar) {   
 	if(lr) { var.rect[[v]] <- dia.rect(0,(num.xvar-v+1)*x.scale ,xvars[v],xlim=limx,ylim=limy,...) } else { var.rect[[v]] <- dia.rect(v*x.scale,0,xvars[v],xlim=limy,ylim=limx,...) }
     }
  nvar <- num.xvar
  if(mimic) { f.scale <- limy[2]/(num.xfactors+1)
      x.adj <- 0} else { f.scale <- max(num.xvar +1,num.yvar+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=limx,ylim=limy,e.size=e.size,...)} else {fact.rect[[f]] <- dia.ellipse(f * f.scale ,limy[2]/scale.xaxis,fact[f],ylim=limy,xlim=limx,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 & !mimic) {if(lr){dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$right,labels =factors[v,f],col=((sign(factors[v,f])<0) +1),lty=((sign(factors[v,f])<0) +1),adj=(v %% 2)) 
    			} else {dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$top,labels =factors[v,f],col=((sign(factors[v,f])<0) +1),lty=((sign(factors[v,f])<0) +1), adj = (v %% 2)) 
    			}
    		} else {dia.arrow(to=fact.rect[[f]]$left,from=var.rect[[v]]$right,labels =factors[v,f], adj = (v %% 2), col=((sign(factors[v,f])<0) +1))} }
                                    }  else {
                if (factors[v,f] !="0") {
               if (!regression & !mimic) { if(lr) {dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$right,labels =factors[v,f],adj = (v %% 2)) } else {dia.arrow(from=fact.rect[[f]],to=var.rect[[v]]$top,labels =factors[v,f],adj = (v %% 2))} 
    			} else {if(lr) {dia.arrow(to=fact.rect[[f]],from=var.rect[[v]]$right,labels =factors[v,f],adj = (v %% 2))} else {dia.arrow(to=fact.rect[[f]],from=var.rect[[v]]$top,labels =factors[v,f],adj = (v %% 2))}
    			   } }
                                    } }
                              } 
      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 & !mimic) {  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 }
                    }  
   }  else {nvar <- 0}
    

 #now, if there is a ymodel, do it for y model 
  if(!is.null(ymodel)| !is.null(Ry)) { 
  	if(lr) { y.adj <-  min(0,(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} 
   	 y.scale <- max(num.xvar +1,num.yvar+1)/(num.yvar+1)
   	 
        for (v in 1:num.yvar) { if(lr){   var.rect[[v+num.xvar]] <- dia.rect(limx[2]-y.curves-errors/2,limy[2]-v + y.adj,yvars[v],xlim=limx,ylim=limy,...)} else {
                                     var.rect[[v+num.xvar]] <- dia.rect(v * y.scale,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(!mimic) {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=limx,ylim=limy,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=limy,xlim=limx,e.size=e.size,...)}
   		  } else {fact.rect[[f+num.xfactors]] <- fact.rect[[f]]
   		 }
     		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(y.factors[v,f]) > cut))) {
     		     if(lr) { dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$left,labels =y.factors[v,f],col=((sign(y.factors[v,f])<0) +1),lty=((sign(y.factors[v,f])<0) +1),adj = (v %% 2))} else {
     		               dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$bottom,labels =y.factors[v,f],col=((sign(y.factors[v,f])<0) +1),lty=((sign(y.factors[v,f])<0) +1),adj = (v %% 2) )}
     		     }
                                    }
                   } else {if(factors[v,f] !="0")  {if(lr) {dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$left,labels =y.factors[v,f],adj = (v %% 2)) } else {
                                                            dia.arrow(from=fact.rect[[f+num.xfactors]],to=var.rect[[v+num.xvar]]$bottom,labels =y.factors[v,f],adj = (v %% 2))
                   }
                   }
             }}
                             } 
                       
  
  	if (num.yfactors ==1) { lavaan[[num.xfactors +1 ]] <-   paste(fact[num.xfactors +1], "=~")  
    for (i in 1:num.y) { sem[k,1] <- paste(fact[1+num.xfactors],"->",yvars[i],sep="")
                        lavaan[[num.xfactors +1]] <-  paste0(lavaan[[num.xfactors +1]], ' + ', yvars[i]) 
                           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 (f in 1:num.yfactors) {  lavaan[[num.xfactors +f ]] <-   paste(fact[num.xfactors +f], "=~")  
                     for (i in 1:num.y) {
                    if( (y.factors[i,f] !="0")  && (abs(y.factors[i,f]) > cut )) {
                          lavaan[[num.xfactors +f]] <-  paste0(lavaan[[num.xfactors +f]], ' + ', yvars[i]) 
                           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=4) } 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] ) & (is.numeric(Phi[i,j]) && abs( Phi[i,j]) > 0)) {
                         
                                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="")
                                                     	 lavaan[[num.xfactors +num.yfactors +1]] <- paste(fact[i], "~~", fact[j])} 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="")
                                                      		lavaan[[num.xfactors +num.yfactors +k]] <- paste(fact[j], "~", fact[i])
                                                      		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="")
                                                lavaan[[num.xfactors +num.yfactors +k]] <- paste(fact[i], "~", fact[j])
                                                sem[k,2] <-  paste("rF",i,"F",j,sep="")
                                                       } 
                                                     	} } else { 
                             k <- k -1 #because we are skipping this one                        	
                           # lavaan[[num.xfactors +num.yfactors +k]] <- paste(fact[j], "~~", fact[i])
                           # 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 ))) {
           #We want to draw an arrrow, but if it is numeric, we need to figure out the sign   
           col <- 1
           if((is.numeric(Phi[j+num.xfactors,i])  &   (Phi[j+num.xfactors,i] < 0))) col <- 2      
                       dia.arrow(from=fact.rect[[i]],to=fact.rect[[j+num.xfactors]],Phi[j+num.xfactors,i], col=col, lty=col)
                       sem[k,1]  <- paste(fact[i],"->",fact[j+num.xfactors],sep="")
                      lavaan[[num.xfactors +num.yfactors +k]] <- paste(fact[j+num.xfactors], "~", fact[i]) } else {
                       k <- k-1
                      # sem[k,1]  <- paste(fact[i],"<->",fact[j+num.xfactors],sep="")
                       # lavaan[[num.xfactors +num.yfactors +k]] <- paste(fact[j+num.xfactors], "~~", fact[i])}
                       
                       # 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)) }
   }