I want to do post-hoc analysis on the individual utility scores (AND relative importance scores) obtained from the Sawtooth Software, to find the association of these utilities with socio-demographic variables (e.g. age, gender..). Since I am not familiar with Bayesian analysis, I am considering three options:
1) perform MANOVA's:
Dependent variable = utilities of the 4 levels of attribute 1
Independent variable = income w/6 levels
For example, H0 = the utilities for the different types of fish (dependent variable, attribute 1) do not differ significantly among income groups (independent variable, 6 lvls).
2) Multivariate regression, where I test multiple dependent variables (utilities of attribute 1 levels 1,2,3,4) at once, against several independent variables (income, age, gender)
For example, H0 = there is no effect of gender, age and income on the utilities (preference?) for the different fish species.
3) perform ANOVA on the relative importance scores:
Dependent variable = relative importance score of the attribute price
Independent vairbale = income w/6 levels
For example, H0 = The attribute price is equally important among respondents with different incomes.
Besides formulating the hypotheses, are these approaches correct? If yes, what exactly are the limitations vs. Bayesian statistics? If no, what should I do instead?