# Binary or multinomial logit?

I am having some doubts on whether I should use binary or multinomial logit. I am modelling product choice. The dependent variable is the choice of either shampoo or toothpaste. Although my dependent variable has two outcomes, I am wondering whether it is appropriate to use multinomial logit instead of binary.

The case is that the customer does not choose among these two products, but among the whole assortment. And I have taken a sample for only 2 products. Do you think I should use the multinomial logit?

• You'd use a binary logit (=logistic regression) if the choices were mutually exclusive. Is it possible that someone buys both shampoo and toothpaste? – Hong Ooi Jul 30 '13 at 11:58
• Yes, i also thought of that. I am actually modelling another products ( anti-acne and medical shampoo) that appear to be mutually exclusive. I ran market basket analysis first to see if they are sold together and they are not. Then I guess its ok to use binary logit. Thanks a lot :) But what if they are not mutually exclusive? There will be some bias in results i guess.. – Ve LLy Jul 30 '13 at 12:09
• Please amend your question, then, to fully reflect what you are trying to do. It sounds like you might be analyzing all of the choices a consumer could make - that is a different problem from the one you posted. – Peter Flom - Reinstate Monica Jul 30 '13 at 12:34
• The whole assortment consists of 67 aggregated product categories. My whole idea is to filter the categories of interest ( shampoo and toothpaste for example) and to see what influences the choice of either shampoo or toothpaste (or both). But If I want to test the option for not buying any of them, I don't know how to do this. The problem is that my independent variables are limited - day and time of purchase. And I am trying to test how the seasons and different times of the day ( morning, afternoon, and evening) influence the purchase probability of certain products. – Ve LLy Jul 30 '13 at 12:47

## 1 Answer

In addition to @HongOoi 's point, could a person buy neither ? Then you;d have four choices:

Both
Toothpaste
Shampoo
Neither


It's not exactly clear what your sample is, but it seems to me you have to have these four choices. In that case, multinomial logit is correct.

However, if your sample includes only people who bought one or the other but not both, you could use (ordinary) logistic. Then you would be comparing people who bought toothpaste to people who bought shampoo.

• I agree with @Peter_Flom. It is usually important to include in the model the option of not buying anything. This makes a third option and it is therefore better to have a multinomial outcome model. – PAC Jul 30 '13 at 12:31