Why can't I do a 3 variable CFA with lavaan on R?

Question

Everything works just fine when I have 4 variables or more. But I thought the minimum for a CFA or EFA was 3 variables. When I run the code, it gives me 0's for all the parameters that estimate if it's a good fit or not.

For this purpose, i will use the USArrests database.

library(lavaan)

d<- USArrests

abc <- 'abc =~  Murder + Assault + Rape'

fit <- lavaan::cfa(abc, data=d, missing = "FIML", estimator = "MLR")

summary(fit, fit.measures=TRUE)

This is where I'm running into an issue. If I add another variable to the abc model like UrbanPop, everything works and I will be able to get the CFI, RMSEA and so on. But sometimes I don't have a fourth one and still want to see if they're a good fit.

Results for 4 variables

Model Test User Model:
                                               Standard      Robust
  Comparative Fit Index (CFI)                    0.910       0.923
  RMSEA                                          0.281       0.221
  SRMR                                           0.073       0.073

And every time I use 3 variables regardless of the dataframe I get this :

Model Test Baseline Model:

  Comparative Fit Index (CFI)                    1.000       1.000
  RMSEA                                          0.000       0.000
  SRMR                                           0.000       0.000

Thank you!

Should be good now. @user2554330 – Em Manuel Oct 19 '22 at 20:58 — Em Manuel, Oct 19 '22 at 20:58

score 2 · Accepted Answer · answered Oct 20 '22 at 08:36

I thought the minimum for a CFA or EFA was 3 variables. When I run the code, it gives me 0's for all the parameters that estimate if it's a good fit

A 1-factor CFA with 3 indicators is just-identified (df = 0) when no errors correlate. If you have df = 0, then your model provides no opportunity for the data to falsify the model. The fit statistic is thus 0 because fit is (arbitrarily) perfect in a just-identified model. Introductory SEM / CFA textbooks discuss identification and fit in more detail, e.g.,

Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford.

Very interesting thank you ! What you would you recommend then if I only have 3 variables that seem to underline a common factor ? Other than seeing if they correlate, my exploratory analysis is trying to estimate their fit. — Em Manuel, Oct 20 '22 at 14:56

Why can't I do a 3 variable CFA with lavaan on R?

1 Answers1