I have run individual analyses for a lot of the dependent variables, for example binary logistic regressions for the dichotomous outcome variables, and ANOVAs for continuous. I also ran a principal components analysis on the questionnaire items, however, the number of extracted factors was greater than the number of scales/subscales (around 20). When scales were analysed individually, they all had acceptable reliabilities > 0.7, and were mostly normally distributed, so I'm not quite sure why this is.
Ideally however, the goal is to be able to combine both observed behavioural outcomes and latent factors from the questionnaires into a singular model with the IV as a predictor. The sample size is too small for SEM, which would be my first choice.
Although I have some hypotheses about how the outcome variables relate to each other, I do not have hypotheses about all. Of course, I can make some informed predictions based on theory, but not for all possible combinations of variables, and in fact, exploring these relationships is part of the goal of the experiment. Nor is an exploratory factor analysis entirely appropriate, as I have a predictor variable and am also interested in the relationships between outcome variables, as well as already have some a priori hypotheses about relationships. Essentially, I want to look at multiple (mediated?) relationships, for which some combinations of variables I already have a priori hypotheses, but not all. In general, I would hypothesise that the latent psychological factors are influencing participants observed behaviours.
Given SEM is inappropriate (due to the low sample), then I am unsure what other statistical method exists which could combine multiple dependent variables and mediator relationships in the way I want. I know path analysis can be done with smaller samples, but as far as I know it doesn't allow for causal relationships or latent factors, such as what are being captured by the questionnaires. A MANOVA combining all the dependent variables would be possible, but I'm not sure how to follow up a significant model. Individual ANOVAS are inappropriate, as there are too many outcomes, and they are related to each other. I briefly looked into discriminant analysis, but I am very unfamiliar with this method so don't know if this is appropriate. I'm also concerned about combining the continuous outcomes with binary outcomes, as well as combining observed (behavioural) and latent (self-report questionnaires) variables in a MANOVA model.
So basically, given I have one independent variable, and multiple, correlated, dependent variables, some continuous and some dichotomous, what is the most appropriate way to analyse the data in order to achieve my goals?