[R] Confirmatory Factor Analysis in R? SEM?

John Fox jfox at mcmaster.ca
Thu Jan 29 05:19:47 CET 2004

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 
along with the corresponding sem commands.

I hope that this helps,

At 01:21 AM 1/29/2004 +0000, Arnab mukherji wrote:
>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
>x2<-rbinom(200, 20, 0.75)
>dat<-as.data.frame(x1 =x1, x2 = x2, x3 = x3, x4 = x4)
>v.c<-cor(dat,use = "complete.obs")
>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.

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

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