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?

- ANOVA for ZCD utilities: do I do 4 ANOVA's, one for each level? (accounted for error)

- Can I use pearson's R for continuous variables e.g. age?

- Multivariate regression is also not appropriate (like MANOVA)?

- What is the appropriate Bayesian modelling technique to check for associations or to make predictions?

Thanks again!