Hello Md Musfiqur,

Given that your outcome is a nominal variable with 4 levels, it would appear that multinomial (logistic) regression is likely an appropriate approach.

Good luck with your work.

David Morse Thank you for your suggestion. My concern is that will it be statistically correct if I consider an ordinary variable to predict a nominal outcome. I have not found any example where ordinal variable has been used to predict nominal outcome

You can opt for either: (a) ordinal model solutions; or (b) recasting all categorical variables (whether ordinal or not) having more than two levels into k - 1 dummy variates (where k is the number of levels/categories).

David Morse Thank you for your response.

If I have binary variable gender(male/female, female reference variable with 0 dummy variable ), age(cont variable), household income ( categorized as for say 0-100 usd=IncA,0101-200=IncB, >200 USD=IncC with each group separated in three columns receiving 0 if does not belongs to group and 1 if belongs to a particular group ), ordinal variable of safety and convenience where direct ranked value given by users will be used. If I get 4 for level of safety, 3 for convenience from a user, I will use 4 and 3 for the safety and convenience,

Then, I can think about the utility model for a mode (Y),

utility(bus)=a+b1* (male)+b2(age)+b3*(rank of safety)+ b4*(convenience)+

b5 * (incB)+b6 * (incC)

Have I got your suggestion correctly?

Hello again, Md Musfiqur Rahman Bhuiya ,

Yes, that's basically it. Please note that if the safety and convenience values were forced choice (had to be ranked, with the others, such that each was given a unique score by a respondent), then they will be negatively correlated with one another. If you instead meant that respondents rated each characteristic on a 1-5 scale (and therefore, that each could have been given the same rating by a respondent), then the two scores might or might not be correlated.

There are some alternate ways to handle the rank/rating scores (other than treating them as pseudo-continuous, which the currently proposed model will do). One option would be dummy code them; another would be to collapse them into "high rating/ranking" (e.g., say 4 or 5), or "low rating/ranking" (the other values). I don't know how little or how much distortion the pseduo-continuous approach would induce; that would be an empirical question for your specific data set.

"Utility" is the chosen mode of transportation, yes? If so, multinomial logistic regression is probably the preferred path.