structure.diagram: Draw a structural equation model specified by two measurement models and a structural model

Description

Graphic presentations of structural equation models are a very useful way to conceptualize sem and confirmatory factor models. Given a measurement model on x (xmodel) and on y (ymodel) as well as a path model connecting x and y (phi), draw the graph. If the ymodel is not specified, just draw the measurement model (xmodel + phi). If the Rx or Ry matrices are specified, show the correlations between the x variables, or y variables.

Perhaps even more usefully, the function returns a model appropriate for running directly in the sem package written by John Fox or the lavaan package by Yves Rosseel. For this option to work directly, it is necessary to specfy that errrors=TRUE.

Input can be specified as matrices or the output from fa, factanal, or a rotation package such as GPArotation.

For symbolic graphs, the input matrices can be character strings or mixtures of character strings and numeric vectors.

As an option, for those without Rgraphviz installed, structure.sem will just create the sem model and skip the graph. (This functionality is now included in structure.diagram.)

structure.diagram will draw the diagram without using Rgraphviz and is probably the preferred option. structure.graph will be removed eventually.

lavaan.diagram will draw either cfa or sem results from the lavaan package. It has been tested for cfa, sem and mimic type output. It takes the output object from lavaan and then calls structure.diagram.

Usage

structure.diagram(fx, 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", ...)
structure.graph(fx,  Phi = NULL,fy = NULL, out.file = NULL, labels = NULL, cut = 0.3, 
   errors=TRUE, simple=TRUE,regression=FALSE, size = c(8, 6), 
    node.font = c("Helvetica", 14), edge.font = c("Helvetica", 10), 
    rank.direction = c("RL", "TB", "LR", "BT"), digits = 1, 
     title = "Structural model", ...)
structure.sem(fx,  Phi = NULL, fy = NULL,out.file = NULL, labels = NULL,
     cut = 0.3, errors=TRUE, simple=TRUE,regression=FALSE)
lavaan.diagram(fit,main,e.size=.1,...) 
sem.diagram(fit,main="A SEM from the sem package",...)
sem.graph(fit,out.file=NULL,main= "A SEM from the sem package",...)

Value

sem: (invisible) a model matrix (partially) ready for input to John Fox's sem package. It is of class ``mod" for prettier output.
lavaan: (invisible) A model specification for the lavaan package.
dotfile: If out.file is specified, a dot language file suitable for using in a dot graphics program such as graphviz or Omnigraffle.

A graphic structural diagram in the graphics window

Arguments

fx: a factor model on the x variables.
Phi: A matrix of directed relationships. Lower diagonal values are drawn. If the upper diagonal values match the lower diagonal, two headed arrows are drawn. For a single, directed path, just the value may be specified.
fy: a factor model on the y variables (can be empty)
Rx: The correlation matrix among the x variables
Ry: The correlation matrix among the y variables
out.file: name a file to send dot language instructions.
labels: variable labels if not specified as colnames for the matrices
cut: Draw paths for values > cut
fit: The output from a lavaan cfa or sem
errors: draw an error term for observerd variables
simple: Just draw one path per x or y variable
regression: Draw a regression diagram (observed variables cause Y)
lr: Direction of diagram is from left to right (lr=TRUE, default) or from bottom to top (lr=FALSE)
e.size: size of the ellipses in structure.diagram
main: main title of diagram
size: page size of graphic
node.font: font type for graph
edge.font: font type for graph
rank.direction: Which direction should the graph be oriented
digits: Number of digits to draw
title: Title of graphic
...: other options to pass to Rgraphviz

Author

William Revelle

Details

The recommended function is structure.diagram which does not use Rgraphviz but which does not produce dot code either.

All three structure function return a matrix of commands suitable for using in the sem or lavaan packages. (Specify errors=TRUE to get code that will run directly in the sem package.)

The structure.graph output can be directed to an output file for post processing using the dot graphic language but requires that Rgraphviz is installed.

lavaan.diagram will create sem, cfa, or mimic diagrams depending upon the lavaan input.

sem.diagram and sem.graph convert the output from a simple CFA done with the sem package and draw them using structure.diagram or structure.graph. lavaan.diagram converts the output (fit) from a simple CFA done with the lavaan package and draws them using structure.diagram. The figure is organized to show the appropriate paths between:

The correlations between the X variables (if Rx is specified)
The X variables and their latent factors (if fx is specified)
The latent X and the latent Y (if Phi is specified)
The latent Y and the observed Y (if fy is specified)
The correlations between the Y variables (if Ry is specified)

A confirmatory factor model would specify just fx and Phi, a structural model would include fx, Phi, and fy. The raw correlations could be shown by just including Rx and Ry.

lavaan.diagram may be called from the diagram function which also will call fa.diagram, omega.diagram or iclust.diagram, depending upon the class of the fit.

Other diagram functions include fa.diagram, omega.diagram. All of these functions use the various dia functions such as dia.rect, dia.ellipse, dia.arrow, dia.curve, dia.curved.arrow, and dia.shape.

Examples

Run this code


#A set of measurement and structural models
#First set up the various matrices
fx <-  matrix(c(.9,.8,.7,rep(0,9), .6,.7,-.8,rep(0,9),.5,.6,.4),ncol=3)
fy <- matrix(c(.9,.8,.6,rep(0,4),.6,.8,-.7),ncol=2)
Phi <- matrix(c(1,.35,0,0,0,
                .35,1,.5,0,0,
                0,.5, 1,0,0,
                .7,-.6, 0, 1,0,
                .0, 0, .4,0,1 ),ncol=5,byrow=TRUE)
#now draw a number of models 
f1 <- structure.diagram(fx,main = "A measurement model for x")
f2 <- structure.diagram(fx,Phi, main = "A measurement model for x")  
f3 <- structure.diagram(fy=fy, main = "A measurement model for y") 
f4 <- structure.diagram(fx,Phi,fy,main="A structural path diagram")            
f5 <- structure.diagram(fx,Phi,fy,main="A structural path diagram",errors=TRUE)

#a mimic model
fy <- matrix(c(.9,.8,.6,rep(0,4),.6,.8,-.7),ncol=2)
fx <- matrix(c(.6,.5,0,.4),ncol=2)
mimic <- structure.diagram(fx,fy=fy,simple=FALSE,errors=TRUE, main="A mimic diagram")

fy <- matrix(c(rep(.9,8),rep(0,16),rep(.8,8)),ncol=2)
structure.diagram(fx,fy=fy, e.size=.05)

#symbolic input
X2 <- matrix(c("a",0,0,"b","e1",0,0,"e2"),ncol=4)
colnames(X2) <- c("X1","X2","E1","E2")
phi2 <- diag(1,4,4)
phi2[2,1] <- phi2[1,2] <- "r"
f2 <- structure.diagram(X2,Phi=phi2,errors=FALSE,main="A symbolic model") 

#symbolic input with error 
X2 <- matrix(c("a",0,0,"b"),ncol=2)
colnames(X2) <- c("X1","X2")
phi2 <- diag(1,2,2)
phi2[2,1] <- phi2[1,2] <- "r"
f3 <- structure.diagram(X2,Phi=phi2,main="an alternative representation",e.size=.4)

#and yet another one
X6 <- matrix(c("a","b","c",rep(0,6),"d","e","f"),nrow=6)
colnames(X6) <- c("L1","L2")
rownames(X6) <- c("x1","x2","x3","x4","x5","x6")
Y3 <- matrix(c("u","w","z"),ncol=1)
colnames(Y3) <- "Y"
rownames(Y3) <- c("y1","y2","y3")
phi21 <- matrix(c(1,0,"r1",0,1,"r2",0,0,1),ncol=3)
colnames(phi21) <- rownames(phi21) <-  c("L1","L2","Y")
f4 <- structure.diagram(X6,phi21,Y3)

###the following example is not run but is included to show how to work with lavaan
# \donttest{
library(lavaan)
mod.1 <- 'A =~ A1 + A2 + A3 + A4 + A5
         C =~ C1 + C2 + C3 + C4 + C5
         E =~ E1 +E2 + E3 + E4 +E5'
fit.1 <- sem(mod.1,psychTools::bfi[complete.cases(psychTools::bfi),],std.lv=TRUE)
lavaan.diagram(fit.1)   #a normal cfa

#compare with
f3 <- fa(psychTools::bfi[complete.cases(psychTools::bfi),1:15],3)
fa.diagram(f3)


#a sem model
mod.2 <- 'A =~ A1 + A2 + A3 + A4 + A5
         C =~ C1 + C2 + C3 + C4 + C5
         E =~ E1 +E2 + E3 + E4 +E5
         E ~ A + C '        
  
fit.2 <- sem(mod.2,psychTools::bfi[complete.cases(psychTools::bfi),],std.lv=TRUE)
lavaan.diagram(fit.2, cut=0,simple=FALSE,main="sem  model")  # A SEM Model 


#a mimic model         
mod.3 <- 'A =~ A1 + A2 + A3 + A4 + A5
         C =~ C1 + C2 + C3 + C4 + C5
         E =~ E1 +E2 + E3 + E4 +E5
         A ~ age + gender
         C ~ age + gender
         E ~ age + gender'

fit.3 <- sem(mod.3,psychTools::bfi[complete.cases(psychTools::bfi),],std.lv=TRUE)
lavaan.diagram(fit.3, cut=0,simple=FALSE,main="mimic model", e.size=.03)




# }
# and finally, a regression model
X7 <- matrix(c("a","b","c","d","e","f"),nrow=6)
f5 <- structure.diagram(X7,regression=TRUE,main = "Regression model")

#and a really messy regession model
x8 <- c("b1","b2","b3")
r8 <- matrix(c(1,"r12","r13","r12",1,"r23","r13","r23",1),ncol=3)
f6<- structure.diagram(x8,Phi=r8,regression=TRUE,main="Regression model")

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