Using a survey I asked participants to state their top 3 choices of positive aspects of their environment (a list of 10) and top 3 negative aspects of their environment (another list of 10).

Since they could choose 3, (not one) these features are not mutually exclusive by case anymore.

The dependent variable, e.g. satisfaction with the environment, is a captured on continuous scale.

I want to test the relationship between these selected positive and negative features of environment and how satisfied people are with it. I considered running multiple regression but realized that I cannot convert the dichotomous categories to dummy-variables as the condition for inclusion of dummy variables in a multiple regression is that they are mutually exclusive (Cohen et al 2003). In this case each participant selected 3.

1. What are my options in terms of testing which features (of the environment, when selected) predict satisfaction? or are strongly related to satisfaction?

2. If it is possible to account for co-variates, or confounding variables as the next step?

Cohen et al 2003 also caution that if not-mutually-exclusive categories are entered in a multiple regression analysis: "The B coefficients will no longer readily reproduce the original Y means of the groups as in the analyses. Instead, each B will represent the mean difference between the group coded 1 and the reference group from each of which has been partialed the effects of the overlap in group membership. Other coefficients such as partial and semipartial correlations will necessarily be similarly partialed for overlap among the groups. Interpretation of the variables in such cases needs to be done with extreme care to avoid erroneous conclusions."

3. If I am to go on with regression using all categories from one variable at a time, what should I be cautious of? What does partialed effects mean?

4. If I was to split my dependent variable into 2 (satisfied not satisfied) categories, could I run another kind of analysis?

Ref: Cohen, J., et al. (2003). Categorial or Nominal Independent Variables. Applied multiple regression/correlation analysis for the behavioral sciences. J. Cohen, P. Cohen, S. G. West and L. S. Aiken. London, England: Taylor & Francis Group.