Non-positive definite matrix and second order confirmatory factor analysis


New Member
For my research I'm using SEM to model the relation between a couple of variables. All scales have been used in a 7 point likert format and most have been validated before in other research. In my dataset however, I have my doubts whether some these scales are truly measuring different concepts, because all measures seem to correlate highly with plotted in a scatterdot matrix (with averaged version of all the scales). This is the reason I want to do a confirmatory factor analysis. I have 10 latent variables and 40 observed variables. Each latent variable has between 3-6 observed variables. I have a little less than 300 participants and no missing variables.

One of the scales is trust, which consists of the subscales ability, integrity and benevolence. In the literature there is mentioned that trust is best modeled as a second-order factor, as they represent components of trust. I'm not completely sure if this means I should do it as well when doing a confirmatory factor analysis or only when using it in regular models. As the sublatent variables are still factors of their own.
If I should use a second order latent variable for trust a cfa, I am not completely sure how the model should look. Right now I modeled it by letting benevolence, integrity and ability covariate and trust covariate with the other latent variables. Another possibility I thought of was to replace ability, integrity and benevolence with a single latent variable trust and add all their observed variables into this one. This would give trust a total of 11 observed variables.

I ran a cfa (in R lavaan package) with and without trust as a second order variable, but both times I got the message the covariance matrix of the latent variables was not positive definite. I read there are some techniques to deal with this and one of them is dropping observed variables. For most latent variables, I could easily drop one or two variables, as these concepts are often measured with fewer items than I used, however is there a way to know which to try to drop first? Additionally does getting a non-positive definite support my idea that the variables seem to be highly correlated? And if so, is this evidence of such a level I can mention it in my thesis? if I can rule out most other explanations.