I think the best way for me to ask this is with an example:
Let's say this is my design...
Ice Cream Flavor
I’m interested in simulating choices between ice cream and cookies. I have a 3-group LCA analysis I want to work with.
Item type raw utilities: +2.06 ice cream, -2.06 cookie
Ice cream flavor raw utilities: -0.08 chocolate, -0.79 gingerbread, +0.79 strawberry
Cookie flavor raw utilities: +0.11 sugar, +0.11 gingerbread, -0.22 snickerdoodle
Cookie size raw utilities: +0.37 big, -0.37 small
When simulating each possible ice cream vs. cookie scenario, the probability of selecting ice cream in this group is between 0.97 - 0.99.
This makes sense to me. Item type is most important to this group. They would almost always choose ice cream, regardless of cookie characteristics.
Item type raw utilities: -6.05 ice cream, +6.05 cookie
Ice cream flavor raw utilities: +4.09 chocolate, +3.61 gingerbread, -7.70 strawberry
Cookie flavor raw utilities: +8.96 sugar, -4.79 gingerbread, -4.17 snickerdoodle
Cookie size raw utilities: +0.16 big, -0.16 small
When simulating each possible ice cream vs. cookie scenario, the probability of selecting ice cream in this group is 0.00 - 0.04
My question is how to reconcile this with the relative importances. Why is item type not also reflected as the most important attribute for this group? It seems like from the simulation projection, people in this group nearly always select cookie over ice cream. Everything else only makes up for 4% of the variance.
Any help is thinking this through is appreciated! Thanks!