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find the effect of variables on utilities

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?
asked Apr 6 by ML (120 points)

1 Answer

0 votes
I think most folks would go the ANOVA route - for both the importances and the transformed (ZCD utilities).  We use the transformed utilities for these because the ZCD transformation is an attempt to remove the logit scale factor confound.  

I'd probably not use MANOVA, because it's null hypothesis has to do with a linear combination of the dependent variables - MANOVA is NOT a multiple test version of ANOVA.  I would account for experiment-wise error in your ANOVAs, using an appropriate post-hoc test.
answered Apr 6 by Keith Chrzan Platinum Sawtooth Software, Inc. (102,150 points)
Thank you Keith for your quick response! Some additional questions:
- 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!
-You'll get a singularity if you include all the levels of an attribute, right?
-We have a good bit about proper Bayesian testing for differences in the Statistical Testing chapter of our Becoming An Expert in Conjoint Analysis book