Some questions about G Index correlation coefficients matrix

[xiaojin]

Dear Ngene experts:
Thank you very much for your previous reply. Now I still encountered some questions. If I can get your help, I would appreciate it very much.

I am doing an unlabeled D-efficient design, and my questions are:
1. I found that some papers use G Index correlation coefficients matrix to judge whether the design has orthogonality. I want to ask what requirements should the value of G Index correlation coefficients matrix meet, only then can we say the design has achieved some level of orthogonality?
2. In addition to the value of B-estimate , some papers will use MNL utilities value to judge whether the design meets the utility balance. If the MNL utility value of alternatives 1 is 1.12 and the utility value of alternatives 2 is -0.12 in one choice situation, can this difference be regarded as basically meeting the utility balance? And how big is the difference that can not be counted as utility balance?

Thank you again for your help!

[Michiel Bliemer]

First of all, neither orthogonality nor utility balance is a requirement for a good design for choice experiments, so I am not sure why you would want to focus on these measures.

A design is orthogonal if each attribute level combination across each 2 attributes appears equally across the design. If a design is orthogonal, the correlation between any two attributes will be zero. Note that correlations can be zero without the design being orthogonal. Even if correlations are very small, the design is not orthogonal, orthogonality is a very strict constraint. Given that orthogonality is not important for choice experiments, having correlations is fine.

Perfect utility balance means that utilities across alternatives are identical. There is no exact definition of utility balance and whether the example you refer to is considered utility balanced or not. What we know is that design that satisfy perfect utility balance are very bad; it is like flipping a coin when selecting an alternative because they are all equally preferred. More efficient is to have some alternatives more preferred than others (without being dominant). A B-estimate between 0.7 and 0.9 reported in Ngene is often consistent with high efficiency. In your example, choice probabilities are 0.78 and 0.22, which results in a B-estimate for that choice task of 0.7. I would consider this a good utility balance.

Michiel

[xiaojin]

Dear Michiel,
Thank you for your reply.
I still have some doubts, because in some papers, I saw that some people use G-index correlation coefficients matrix to explain the orthogonality. I want to know how to observe and explain the G-index correlation coefficients matrix. There is no relevant explanation in Ngene operation manual.

And in my design, the MNL utility value of alternatives 1 is 1.12 and the utility value of alternatives 2 is -0.12 in one choice situation, I want to know how to calculate the result with choice probabilities 0.78 and 0.22.

I am a newcomer to the DCE. The questions I asked may be too basic. Thank you again for your help!

Best wishes!

[Michiel Bliemer]

I do not know how to interpret a G-index, I always use the Pearson correlation coefficient myself. Ngene simply reports all correlation coefficients so the user can choose which one they prefer. I suggest you contact tha authors of the article to ask why they use the G-index and how they interpret it. Note that orthogonality cannot be judged by a correlation coefficient as I mentioned in my post, it is possible that correlations are zero while the design is not orthogonal.

The formula for logit choice probabilities is:

P_i = exp(V_i) / sum_j exp(V_j).

Using V_1 = 1.12 and V_2 = -0.12 gives you my reported choice probabilities P_1 and P_2.

Michiel