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.