How does MBC handle missing prices due to non-availability in the Preview Design Matrix?

Question

Hi,

I am analyzing the choice between service providers depending on the availibility of features and the prices thereof. So the choice between provider A, B and C is specified as dependent on the availability (1/0) variable and 5 price points for each feature. In the data file prices are blank when a feature is unavailable but I noticed that in Preview Design Matrix there are zeros when I specify the price effect as linear.

Now I cannot tell MBC that the effects of price values are dependent on the features availability (that I can only do for dependent variables). Does that mean that the zeros are used in the estimation? That is what the programm does when 5 equidistant price points are transformed into -0.5 to 0.5 with zero being one of the points used for estimating the linear parameter. But in my case 0 could be either a transformed or a missing value.

What can I do to still include the effect of the prices of the features rather than just the effect of wether they are there or not?

Thanks,
Alex

Answer 1

Whenever alternative-specific attributes are not applicable to an alternative, CBC and also MBC must have some value in the design matrix.  The zero is the standard way to do that.  It indeed is referenced in the information regarding a non-applicable attribute when determining the total utility (and thereafter the likelihood) of choosing an alternative.  But, whenever it is referenced as a zero it picks up zero utility, so in essence it is "omitted" from affecting the utility of a non-applicable alternative.

Comments

Thank you for the response Bryan.
I'm still somewhat puzzled about the implications this has for the calculation of the alternatives utilities. Doesn't that mean that it has the same impact on utility of, say, option A if it includes a feature X at price level 3 than when feature X is not available at all?  
When the price of feature X is specifyied as linear (and, hence, its levels 1-5 are transformed into the values -.5, -.25, 0, .25, .5) then in the calculation of utility the midlevel price will yield 0 * ß (i.e. the estimated linear parameter) utils. The same happens if the feature is absent and again a 0 (this time for a missing price level) is multiplied with ß in the utility function of option A.
The difference between the two cases is that the availability parameter carries some utility in the first case while it is also set to 0 in absence of the feature.
Am I not right thus far?