I am trying to do some path modelling (i.e. SEM without the estimation of any latent variables).
I am using questionnaire sum-scores in one of my models - where the questionnaire from which scores are derived is Likert-type. The questionnaire in question is the Childhood Trauma Questionnaire. The issue is that, as I understand it, path/sem models expect continuous data as input. But I wonder to what extent are my scores truly continuous? For instance, they appear almost discrete if I plot them on a histogram - almost like ordinal rank data. (See below)
I have seen other papers take sum scores of the same questionnaire I am using as input in a path model. Here is an example. Or in general, other (Linkert type) questionnaires of the same nature, where possible sum-scores range from 5 to 25.
So this seems to be a non-issue, I just don't understand why the models can cope with this data well as opposed to something more "continuous" like e.g. seconds.