I recommend the design of structural equations, Rasch analysis, Response Theory to the dichotomous item, another would be the analysis of binary logistic regression, another type of robust analysis novel for dichotomous data is the network analysis with the Ising estimator for binary data that allows to explore the elements in a systemic way and allows to highlight the most important elements.

In my opinion, the key is the difference between logistic regression and ordinal logistic regression. See the attached notes. Best, David Booth PS you might also consult the many responses to "How do I deal with Likert data?" to understand the problem. for example:

https://www.researchgate.net/post/Which_is_better_ML_with_bootstrapping_or_MLR_estimation_with_non-normal_data

https://www.researchgate.net/post/Is_the_likert_scale_ordinal_nominal_discrete_or_continuous_ratio_Is_it_valid_to_use_one_of_them_as_an_approach_of_another

Best wishes, D. Booth

I agreed with Dr.David Eugene Booth answer.

Dear Dr. David Eugene Booth

Thank you very much. The slides, and the codes associated with them, are a great help. Depending on the type of data I'll explore ordinal regression or multinomial regression.

Best

Dear Christian

Thank you very much for your advice. I didn't know you could use SEM for categorical data. Do you have a reference?

The reference is following

Business Statistics by Examples Fifth edition,

By Terry Sinich