Which test should I use in an experimental study with a questionnaire?

#1
Hi all,
I Need some help with my first experimental study.
I would like to test the influence of different variables (x1, x2...) on an individual's decision to choose option a, b,c,d.
I use a questionnaire, so that there are levels of willing to choose each option: for each option, the individual specifies the likelihood (most likely...not at all).
Let's assume that the sample is big enough and there is a normal distribution. What test should I use?
 
#2
You could use multinomial logistic regression. You would need to

1] simulate the data as binary indicators 0/1 according to the reported probabilities

or

2] modify the maximum likelihood estimation algorithm to handle the reported probabilities directly, instead of binary indicators.

If the respondents always report the probabilities for a-d options as rational numbers, the first approach is easier.