Efficiency for Specific Parameters (Attribute Levels)
Efficiency for Specific Parameters (Attribute Levels)
Sometimes, you may be more concerned about the efficiency of the design for estimating a specific parameter (such as the utility for your client's brand) rather than an overall efficiency of the design across all parameters. Let's assume that your client asked you to implement prohibitions between the client's brand name and other levels. Further assume that the overall relative strength of the design with prohibitions relative to the design without prohibitions is 97%. On the surface, this seems like little overall loss in efficiency. However, you note that the standard error (from the logit report using simulated data) for your client's brand was 0.026 prior to implementing the prohibition, but 0.036 afterward. The relative efficiency of the design with prohibitions relative to the non-prohibited design with respect to this particular attribute level is:
a2/b2
Where b is the standard error of the estimate for the client's brand name after the prohibition and a is the standard error prior to the prohibition. In this case, the relative design efficiency of the prohibited compared to the non-prohibited design with respect to this particular level is:
0.0262/0.0362 = 0.52
And the impact of these prohibitions on estimating your client's brand utility is more fully appreciated.
