# D-efficiency in choice-based conjoint analysis

How to calculate the D-efficiency of experimental designs in conjoint analysis?

Specifically, how do you specify the $X$ and the number of $nBetas$ in this formula:

$$D_e=\frac{|X'X|^{1/nBetas}}{nSets}$$

This question addresses the calculation of D-efficiency for simple experimental designs, but I don't fully understand how to apply it to conjoint designs (where there are different attributes and levels), both alternative-specific and not.

I would appreciate an example.

For those who want to learn about designing of choice experiments (CEs), I would strongly advise to read the documentation of the NGENE software (https://dl.dropboxusercontent.com/u/9406880/NgeneManual112.pdf), which is probably the best software to design CEs.

To answer your question, as indicated by the formulae, you need 2 pieces of information:
1/ What are the preferences (beta) for the attributes (X)?
2/ What is the design of the CE (i.e., content of the choice tasks)?
The tricky part here is to obtain this a priori knowledge about the betas.
By default, a conservative approach consists in assuming that the betas are null.
In this particular case there would be actually very little difference between a D-Efficient design and an orthogonal design.

You can relax this assumption in different ways:
- Run a pilot study to get a rough idea of what might be people preferences for (X).
- Look at the literature and try to find a comparable study - Unlikely to be a good idea.
- Make some pseudo-informed guesses (e.g., one would expect people preferences for product price to be negative - Therefore you could assume that beta_cost follows a negative log-normal distribution ...).