The slopes in the last category are zero. This is all because the multinomial model models log odds, that is, the log of the ratio of a prob for one category versus the last. As the plot on page 497 shows that doesn't mean that the probability of the last category doesn't change with x; it does.
You can change which category comes last.
David James posted on Wednesday, December 23, 2015 - 12:36 am
Thank you for the help and guidance. I really appreciate it!!
Another way I have seen this tackled is by expressing the utilities of the other choice options as differences with respect to the last alternative’s utility. This involves making the parameters of the last choice option enters all other utility functions with the opposite sign by specifying the required linear constraint.
For example: !Multinomial logit model U#1 ON Z1; U#1 ON Z2; U#1 ON (-Z5) (1); U#1 ON (-Z6) (2);
U#2 ON Z3; U#2 ON Z4; U#2 ON (-Z5) (1); U#2 ON (-Z6) (2);
[U#1 U#2]; !alternative-specific constants
What do you think about this approach? Do you foresee any issues.