[R] Confirmatory Factor Analysis in R? SEM?

[Arnab mukherji]

Hi 

Has anyone used R to conduct confirmatory factor analysis?  This email pertains to use of SEM.

For context consider an example: the basic idea is that there are a bunch of observables variables (say study habbits, amount of time reading in the bus, doing homework, helping other do homework, doing follow-up on errors etc.) and one believes that all these variables maybe measured by two or more unobservable constructs... say ability to work hard and ability to follow instructions. If one has empirical evidence from earlier studies which relates similar observable to similar unobservables one wants to do a confirmatory factor analysis to check if the posited relationship holds in the current data being analyzed.

I thought the way out would be to use SEM - the structural equation model library. However, i am not sure how to estimate SEM objects where factors are unobservable. The only discussion pertian to the case of endogenously detemined observable variables.

here is a test case of what i'd like to implement

#example Measurement Model

x1<-runif(200)
x2<-rbinom(200, 20, 0.75)
x3<-runif(200)
x4<-runif(200)
dat<-as.data.frame(x1 =x1, x2 = x2, x3 = x3, x4 = x4)

v.c<-cor(dat,use = "complete.obs")
ind<-upper.tri(v.c)
v.c[ind]<-0 
model.dhp<-matrix (c(
                       "x1 -> HWK", "gam11", NA,
                       "x2 -> HWK", "gam21", NA,
                       "x2 -> FI",  "gam22", NA,
                       "x3 -> HWK", "gam31", NA,
                       "x3 -> F1", "gam32", NA,
                       "x4 -> F1", "gam42", NA),
                       ncol = 3, byrow = TRUE)
These are the Factor loadings i'd like to test for: 
 variable   HWK     FI
 x1         0.75    0
 x2         0.20    0.68
 x3         0.2     0.5
 x4         0       0.24


thanks for any help on this.

Arnab