Qualitative choice analysis:

In  order to analyze discrete data we often  use qualitative choice or discrete choice analysis. This method  of  analysis focuses on  appropriate specification, estimation, and use of models for the probabilities of events, where in most cases, the "event"  is an  individual's choice among a set of alternatives. Thus, it is designed for describing finite valued choice behavior in certain types of situations. These situations arise in a variety of contexts in different areas,  such  as  transportation, energy, telecommunications, housing, criminology, and labor. However, qualitative choice analysis is not applicable universally but  in  certain types of situations. Let us define these situations.

Qualitative choice models may  be used  to model and  analyze situations in  which a decision maker  faces a choice among  a  set of  alternatives meeting  the  following criteria:

I)  The number of alternatives  in the set is finite;

2)  The alternatives are  mutually  exclusive,  i.e.,  if  the  person  chooses one alternative in the set then the person does not choose another alternative; and

3)  The set of alternatives  is exhaustive, i.e.,  all possible alternatives are included, and the person necessarily chooses one alternative  from the set.

Let us  consider the choice of mode of transport for travel to work. The alternatives available could be  three-wheeler, two-wheeler, car, taxi, bus, metro, walk, etc. This need  not  always satisfy the  criteria above. There is a possibility of driving  to the buslmetro stop and then taking public transport. In such a situation the alternatives of three-wheeler, two-wheeler, car, taxi, bus, metro, walk,  etc.  are  not  mutually exclusive as the person  could take both  car and bus. Similarly a consumer's  choice between two different insurance policies offered by  a salesperson does not satisfy the third criterion. The set of alternatives  is not exhaustive, as the consumer may decide to purchase a completely different policy offered by  another salesperson.

Notice that in both  these examples (and in many other similar cases) it is possible to redefine  the  set  of  alternatives such  that the redefined set  satisfies all  the three criteria.  The  choice  between two life insurance  policies  offered  by  a  particular salesperson can be redefined to include a third alternative, nmely, the possibility of choosing neither of  the two  policies.  This  would  make  the  set  of  alternatives exhaustive. Similarly, in  the problem of choosing the mode of transport to work we may redefine the set of alternatives as car only, bus only, metro only, metro with car, etc. This would make the set of alternatives mutually exclusive. Thus, the only truly restrictive criterion  is  the  first one,  i.e.,  the number of alternatives must be  finite. This implies  that any choice situation in which the set of alternatives  can be denoted by a continuous vdiable is not a qualitative choice situaticm.

It  must  be  pointed  out that  the  term  qualitative  choice situation  is  a  bit  of  a misnomer. In  some choice situations  the choice is in regard to "how many" yet they meet the criteria for qualitative choice situations. An  example is the choice of how many cars to own. Assuming that an  individual cannot own more than Jcars, the set of  alternatives  is 0,1,2,.  .  .  ,  J, which  is clearly a finite, exhaustive set of mutually exclusive alternatives.

We shall confine ourselves  to cases of qualitative choice where the set of alternatives is binary, i.e.,  only two alternatives are available.

Let  us  start  with  a  simple example.  An  adult individual has  two  choices:  to work/seek work, (Y = 1), or not  to work, (Y = 0). Assume  for now  that  individual decisions are independent of the decisions  of other household members. The problem may be modeled in several different ways.