I am currently working on running a SEM analysis in Lavaan and I am running into a few problems. Before running the full sem, I intended to run a CFA to replicate the psychometric testing done with this measure I am using. This measure has 24 items, which make up 5 subscales (latent variables), which in turn load onto a total "higher-order" factor. I try to estimate this model in two different ways: (1) A five-factor model (without a higher order factor) in which all 5 subscales are allowed to correlate and (2) a higher-order model with a TOTAL latent variable made up of those 5 suscales.
The first model has five correlated latents (FNR, FOB...FAA) factors, with variance fixed to 1. This model converges without errors and fits the data. The second model also works, as long as I don't specify that the subscales (FNR, FOB..) that make up the FTOTAL latent variable are correlated. However, if I specified that these subscales are correlated (#Residual correlations part), the model still runs but gives me the error "lavaan WARNING: could not compute standard errors! The information matrix could not be inverted. This may be a symptom that the model is not identified." If I remove the residuals correlation from Model 2, the model runs without error. The R code for both is the following:
Model1 <- "
#Measurements model
FNR =~ FNR1 + FNR2 + FNR3 +FNR4 +FNR5
FOB =~ FOB1 + FOB2 +FOB3 +FOB4
FDS =~ FDS1 +FDS2 +FDS3 + FDS4 + FDS5
FNJ =~ FNJ1 + FNJ2 + FNJ3 +FNJ4 + FNJ5
FAA =~ FAA1 + FAA2 +FAA3 + FAA4 +FAA5
#Residual correlations
FAA ~~ FNJ + FOB + FDS + FNR
FNR ~~ FNJ + FOB+ FDS
FNJ ~~ FOB + FDS
FOB ~~ FDS
"
fit5factor <- sem(Model1, data=SEMDATA, std.lv=TRUE)
Model2 <- "
#Measurements model
FNR =~ FNR1 + FNR2 + FNR3 +FNR4 +FNR5
FOB =~ FOB1 + FOB2 +FOB3 +FOB4
FDS =~ FDS1 +FDS2 +FDS3 + FDS4 + FDS5
FNJ =~ FNJ1 + FNJ2 + FNJ3 +FNJ4 + FNJ5
FAA =~ FAA1 + FAA2 +FAA3 + FAA4 +FAA5
FTOTAL =~ FNR + FOB + FDS + FNJ+ FAA
#Residual correlations
FAA ~~ FNJ + FOB + FDS + FNR
FNR ~~ FNJ + FOB+ FDS
FNJ ~~ FOB + FDS
FOB ~~ FDS
"
fitTotal <- sem(Model2, data=SEMDATA, std.lv=TRUE)
This is my first time using SEM and I am not sure what I am doing wrong. Is it not appropriate to specify that these subscales that make up the FTOTAL latent variable are allowed to correlate? I understood from the literature that this is how the 2nd model was supposed to be specified (with the Five factors correlated), given that in the first model the five facets are correlated. However, maybe that is not the case and I should be running model two without the correlations, but I would like to learn the justification for that, and why this is not appropriate.
Thank you all in advance for the help.
You do not need to specify the correlations among first-order factors. The default options of lavaan will correlate them. If do not want to correlate them you can use the orthogonal=T inside the cfa() function.
Model1 <- "
#Measurements model
FNR =~ FNR1 + FNR2 + FNR3 +FNR4 +FNR5
FOB =~ FOB1 + FOB2 +FOB3 +FOB4
FDS =~ FDS1 +FDS2 +FDS3 + FDS4 + FDS5
FNJ =~ FNJ1 + FNJ2 + FNJ3 +FNJ4 + FNJ5
FAA =~ FAA1 + FAA2 +FAA3 + FAA4 +FAA5
"
fit5factor <- sem(Model1, data=SEMDATA, std.lv=TRUE)
Regarding a hierarchical structure, you do not have correlations among first-order factors, since the same latent (i.e. second-order) loads on them:
Model2 <- "
#Measurements model
FNR =~ FNR1 + FNR2 + FNR3 +FNR4 +FNR5
FOB =~ FOB1 + FOB2 +FOB3 +FOB4
FDS =~ FDS1 +FDS2 +FDS3 + FDS4 + FDS5
FNJ =~ FNJ1 + FNJ2 + FNJ3 +FNJ4 + FNJ5
FAA =~ FAA1 + FAA2 +FAA3 + FAA4 +FAA5
FTOTAL =~ FNR + FOB + FDS + FNJ+ FAA
"
fitTotal <- sem(Model2, data=SEMDATA, std.lv=TRUE)
If it solves your problem mark it as solved.