I conducted a survey with almost 400 responses. I have a model in which I set relationships among different variables. One of them is a second-order factor (OP) which I theoretically consider formative (formed by OPA, OPE, OPI and OPO, see pic below).
How should I measure OP? Using the different items of the 4 latent variables? Should I calculate Latent Variable Scores?
This is how I set the model:
model<-'
MOT =~ MOT01+MOT02+MOT03
HAP =~ HAP01+HAP02+HAP03+HAP04
SEN =~ SEN1 + SEN2 + SEN3
WOR =~ WOR1 + WOR2 + WOR3
PER =~ PER1 + PER2 + PER3 + PER4 + PER5
OPA =~ OPA1+OPA2+OPA3
OPE =~ OPE1+OPE2+OPE3
OPI =~ OPI1+OPI2+OPI3
OPO =~ OPO1+OPO2+OPO3
#Second order
OP <~ OPA+OPE+OPI+OPO
#Regressions
SEN~MOT
SEN~HAP
WOR~MOT
WOR~HAP
PER~MOT
PER~HAP
OP~MOT
OP~HAP
OP~SEN
OP~WOR
OP~PER
'
fit_OP<-cfa(model, data=data, estimator="MLM", meanstructure = TRUE)
I therefore get the following warning messages. I assume it is because OP is not adequately measured.
Warning messages:
1: In lav_partable_check(lavpartable, categorical = lavoptions$.categorical, :
lavaan WARNING: automatically added intercepts are set to zero:
[OP]
2: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :
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.
3: In lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, :
lavaan WARNING: could not invert information matrix needed for robust test statistic
Then I extracted the LVS of each of the 4 LV (OPA, OPE, OPI, OPO) and tried to use them to measure OP:
OP =~ OPA_LVS+OPE_LVS+OPI_LVS+OPO_LVS
But I am not confident this is the right approach. I got the following warning:
In lav_samplestats_icov(COV = cov[[g]], ridge = 1e-05, x.idx = x.idx[[g]], :
lavaan WARNING: sample covariance matrix is not positive-definite
I am not sure why is that.
I also tried to measure OP using the original scores:
OP =~ OPA+OPE+OPI+OPO
I did not get any warning this time, but results are a bit confusing and again, I am not sure if that is the correct approach.
I would appreciate any insights on this.
Thank you!!