by johnr » Mon Jun 06, 2016 3:17 pm
Hi Mike
In a situation involving a true no choice situation, the no choice alternative has no attribute levels. In that case, your sources may have misinformed you. Only in a case involving a status quo might the opt out alternative have actual actual levels.
Assuming you do want a no choice as opposed to a status quo, it is important to remember utility is relative, not absolute. By setting the utility of the no choice alternative, the utilities for the SP alternatives will be calculated relative to zero. This is perfectly fine. Consider the following outcome in terms of utility.
U(no) = 0
U(a) = -2
U(b) = 3
The zero for the no choice does not mean it has no utility. It simply means that compared to the utility for a (=-2), it has more utility, but less utility that b. Now consider the role constants play.
U(0) = 0
U(a) = asc1 = -2
U(b) = asc2 = 3
If we re-arrange the ASCs so that it goes into the no-choice, you will get
U(0) = asc1 = 2
U(a) = 0
U(b) = asc2 = 5
which will preserve the relative differences in utility. So you can place an ASC in the no-choice if you want, but it is just re-arranging the deck chairs (hopefully not on the Titanic).
You can place socio-demographics into the SQ alternative (though this is NOT a design question - it is an estimation one). For example
U(0) = theta*gender + ....
U(a) = asc1 + beta1*x1a ...
U(b) = asc2 + beta1*x1b ...
That will simply tell you whether people with different socio-demographic characteristics are either more likely or less likely to choose the no choice alternative (depends on the signs of the parameters).
But unless the no choice alternative has actual attributes that describe it, then something * 0 will in most cases I am aware of, be = 0.
So
U(0) = beta1*x10 ...
U(a) = asc1 + beta1*x1a ...
U(b) = asc2 + beta1*x1b ...
if x1. is price, then for the no-choice alternative, it = 0 unless there is a cost of not choosing, and by my calculations (proof not shown), beta1*0 = 0.
This may cover what you say, that is, they simply don't like a or b. The thing is that you are comparing a and b to nothing at all - they prefer b to having nothing, but prefer nothing to a. The question is what is nothing at all. You can do the above, and assume it is a status quo (I'm an economist, I can assume anything). The problem with this, is that if not choosing means respondents have a status quo alternative in reality and they are sticking wit that, and the levels of the status quo have some distribution over that population in terms of the levels associated with each, then by doing the above you are assuming a form of preference homogeniety for the no choice (it is 0 for everyone), when in fact utility for this alternative might have some distribution over the population, even if the preferences are fixed. That is
U(0) = beta* random variable
means U(0) varies randomly over the population, whereas
U(0) = 0
does not.
So now what if it is a status quo alternative and not a no choice? One form of this (there are others) is described in Section 8.3 of the manual.
John