R help - Jan 2004 - Confirmatory Factor Analysis in R? SEM?

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

Dear Arnab,

You can indeed fit confirmatory factor analysis models with the sem 
package, and ?sem includes an example of a second-order CFI (though I'm not 
sure I see the point of factor-analyzing uncorrelated variables). In factor 
analysis, moreover, the observed variables are functions of the factors, 
not vice-versa (which is how you've specified it). As well, you have to 
define variances and possibly covariances for the factors.

You'll find a simpler example in some lecture notes at 
<http://socserv.socsci.mcmaster.ca/jfox/Courses/soc761/index.html#lecture-notes>,
along with the corresponding sem commands.

I hope that this helps,
  John


At 01:21 AM 1/29/2004 +0000, Arnab mukherji wrote:
>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
-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox