Covariance based SEM and GOF indexes

Question

I have some questions all related to SEM models. I am just estimating a SEM model in R using the function sem. The model looks like this:

SEMmodel <- '
factor1_a =~ x1 + x2 + x3 
factor2_a =~ x39_9 + x39_16 + x39_18 + x39_19 + x39_21
factor3_a =~ x39_5 + x39_6

factor1_b =~ x39_31 + x39_32 + x39_33
factor2_b =~ x39_10 + x39_13 + x39_8 + x39_3

factor1_c =~ x39_1 + x39_2
factor2_c =~ x39_14 + x39_15
factor3_c =~ x39_29 + x39_30 
factor4_c =~ x39_29 + x39_30

a =~ factor1_a + factor2_a + factor3_a
b =~ factor1_b + factor1_b
c =~ factor1_c + factor2_c + factor3_c + factor4_c

# Add some indirect effects between the second level factors and a regression.

#Covariances
factor1_a ~~ factor2_a
factor1_b ~~ factor1_a
factor3_c ~~ factor4_c
factor2_b ~~ factor2_c
'
fit <- sem(SEMmodel, data=data)

I am asked to state whether I use a covariance-based structural equation modeling. I am not able to understand it. Do I use it just because I define the covariances or this is something different?

Moreover, I am asked to report the average variance extracted (AVE) and the composite reliabilities but I don't know which indicators are since I haven't found them anywhere among the goodness of fit indices...

Can somebody help please? Thanks in advance!

Answer 1

I am asked to state whether I use a covariance-based structural equation modeling. I am not able to understand it. Do I use it just because I define the covariances or this is something different?

That is generally what SEM is: analysis of (mean and) covariance structure. The "data" being modeled are the summary statistics, rather than individual data vectors.

AVE and reliability are not fit indices. If they are of substantive interest in your study, you can obtain them using the semTools package by passing your lavaan object to the appropriate functions. Beginning with the upcoming version of semTools (0.5-6), AVE() has its own function, and composite reliability is returned by compRelSEM(). See references on those help pages for more information.

• NOTE: Until version 0.5-6 is available on CRAN, you can find both AVE and composite reliabilities using the (to be deprecated) reliability() function.