```
#The Dwyer Example
Ro <- Dwyer[1:7,1:7]
Roe <- Dwyer[1:7,8]
fo <- fa(Ro,2,rotate="none")
fe <- fa.extension(Roe,fo)
#an example from simulated data
set.seed(42)
d <- sim.item(12) #two orthogonal factors
R <- cor(d)
Ro <- R[c(1,2,4,5,7,8,10,11),c(1,2,4,5,7,8,10,11)]
Roe <- R[c(1,2,4,5,7,8,10,11),c(3,6,9,12)]
fo <- fa(Ro,2)
fe <- fa.extension(Roe,fo)
fa.diagram(fo,fe=fe)
#alternatively just specify the original variables and the extension variables
fe = fa.extend(R, 2, ov =c(1,2,4,5,7,8,10,11), ev=c(3,6,9,12))
fa.diagram(fe$fo, fe = fe$fe)
#create two correlated factors
fx <- matrix(c(.9,.8,.7,.85,.75,.65,rep(0,12),.9,.8,.7,.85,.75,.65),ncol=2)
Phi <- matrix(c(1,.6,.6,1),2)
sim.data <- sim.structure(fx,Phi,n=1000,raw=TRUE)
R <- cor(sim.data$observed)
Ro <- R[c(1,2,4,5,7,8,10,11),c(1,2,4,5,7,8,10,11)]
Roe <- R[c(1,2,4,5,7,8,10,11),c(3,6,9,12)]
fo <- fa(Ro,2)
fe <- fa.extension(Roe,fo)
fa.diagram(fo,fe=fe)
#now show how fa.extend works with the same data set
#note that we have to make sure that the variables are in the order to do the factor congruence
fe2 <- fa.extend(sim.data$observed,2,ov=c(1,2,4,5,7,8,10,11),ev=c(3,6,9,12))
fa.diagram(fe2,main="factor analysis with extension variables")
fa2 <- fa(sim.data$observed[,c(1,2,4,5,7,8,10,11,3,6,9,12)],2)
factor.congruence(fe2,fa2)
summary(fe2)
#an example of extending an omega analysis
fload <- matrix(c(c(c(.9,.8,.7,.6),rep(0,20)),c(c(.9,.8,.7,.6),rep(0,20)),c(c(.9,.8,.7,.6),
rep(0,20)),c(c(c(.9,.8,.7,.6),rep(0,20)),c(.9,.8,.7,.6))),ncol=5)
gload <- matrix(rep(.7,5))
five.factor <- sim.hierarchical(gload,fload,500,TRUE) #create sample data set
ss <- c(1,2,3,5,6,7,9,10,11,13,14,15,17,18,19)
Ro <- cor(five.factor$observed[,ss])
Re <- cor(five.factor$observed[,ss],five.factor$observed[,-ss])
om5 <-omega(Ro,5) #the omega analysis
om.extend <- fa.extension(Re,om5) #the extension analysis
om.extend #show it
#now, include it in an omega diagram
combined.om <- rbind(om5$schmid$sl[,1:ncol(om.extend$loadings)],om.extend$loadings)
class(combined.om) <-c("psych","extend")
omega.diagram(combined.om,main="Extended Omega")
#show how to use fa.extend to do regression analyses with the raw data
b5 <- faReg (bfi, nfactors = 5, ov =1:25, dv =26:28)
extension.diagram(b5)
R <-cor(bfi,use="pairwise")
b5.r <- faReg(R, nfactors = 5, ov =1:25, dv =26:28) # not identical to b5
round(b5$regression$coefficients - b5.r$regression$coefficients,2)
```

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