a) fixed effects multinomial logit model,

b)mixed effects multinomial logit model,

c) fixed effects multinomial probit model, and

d)mixed effects multinomial probit model?

There are three alternatives per question, 16 attributes, and only three attributes are presented in each question. A total of 18 questions. We are interested in modelling individual ID as the random/cluster variable, attributes (A1-A16) as fixed effects, and patient demographic as fixed effects.

Also, my dataset is a balanced fractional factorial design with over 1000 participants who were randomly assigned one of 999 different surveys generated by Sawtooth - so I won't have to worry about sparse data.