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 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. 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, factor.pa, 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 (> .4.0)

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,title,...)

Arguments

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.

a factor model on the y variables (can be empty)

The correlation matrix among the x variables

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)

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

Value

sem(invisible) a model matrix (partially) ready for input to John Fox's sem package. It is of class ``mod" for prettier output.
dotfileIf 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

Details

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

All three function return a matrix of commands suitable for using in the sem package. (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.

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

fx <- matrix(c(.9,.8,.6,rep(0,4),.6,.8,-.7),ncol=2)
fy <- matrix(c(.6,.5,.4),ncol=1)
Phi <- matrix(c(1,0,0,0,1,0,.7,.7,1),ncol=3,byrow=TRUE)
f1 <- structure.diagram(fx,Phi,fy,main="A structural path diagram")

#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")

#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)



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

#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)

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