Are "discrete-like" questionnaire sum-scores acceptable as "continuous" variables in SEM/path models?

Question

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.

Answer 1

1. No real data is really continuous.
2. No method requires truly continuous data for being computed.
3. The question whether measurements are ordinal, interval, nominal or ratio is different from whether data are continuous or discrete. Discreteness in itself is not an indication of ordinality, nor is it theoretically impossible that continuous data are ordinal (except that as said above no real data are truly continuous).
4. The theory behind many methods is based on models for continuous data. This doesn't mean that the real data on which the methods are performed have to be truly continuous. However, certain deviations from the theoretical model assumptions can lead to problems. I don't know what exactly you want to do; I'd worry a bit about binary data or data with just three possible values, but not about the value range that you apparently have. However an issue with the shown histogram may be strong skewness, at least if you want to do something that is based on Gaussian distribution theory, such as confidence intervals for path coefficients (this would be an issue with more "continuous" data as well).