Bayesian Efficiency under panel ML context

[nutterzht123]

Dear Ngene administrators,

Thanks for providing such an excellent tool!

I am trying to generate Bayesian efficiency pivoted design under RP-Panel model. I was able to follow your suggestions from discussions (reference for other userss): http://www.choice-metrics.com/forum/vie ... ?f=2&t=219 and http://www.choice-metrics.com/forum/vie ... ?f=2&t=252, and Bliemer, M. C., & Rose, J. M. (2010). Construction of experimental designs for mixed logit models allowing for correlation across choice observations. Transportation Research Part B: Methodological, 44(6), 720-734.

1. The question I have now is how to decide if the design is efficient enough under rp-panel assumptions. The evaluation will generate a D-error.

2. Should I use the design generated from the evaluation rather than the MNL model?

3. Will the segments not individual specific attribute levels cause bias or inefficiency when applying prospect theory?

Best,
Haotian

[Michiel Bliemer]

1. The lower the D-error the better, but which value of D-error is good enough is case specific and no guidance can be given here. If you are using somewhat reliable parameter priors, then it is best to look at the S-estimates of each parameter and judge whether they can be estimated.

2. I am not sure I understand this question. We advise optimising for an MNL model using (Bayesian) priors and then evaluating the design for a panel mixed logit model. The design under this evaluation is the same as the design generated by the MNL model.

3. Parameter estimates should not be biased by an experimental design, but of course you can loose some efficiency if you estimate a different model than what you optimise for. Note that it is not needed to find the most efficient design so do not worry too much about efficiency, it is more important to ensure that your choice tasks are realistic, are familiar (using individual specific levels), remove dominant alternatives, are not too complex, etc.

Michiel

[nutterzht123]

Thank you, Michiel, for your explanation!

The S-estimates is not supported when using fisher. I am generating a pivoted design. Is there a way to look at S-estimate in this case?

Haotian

[Michiel Bliemer]

S-estimates are calculated by solving the following inequality for N for each attribute k:

beta[k] / (se[k]/sqrt(N)) > t,

where
t = 1.96 for a 95% confidence interval
beta[k] = prior for attribute k
se[k] = standard error for attribute k for a single respondent, which is the square root of the diagonal element of the AVC matrix

In other words,

N > (t*se[k] / beta[k])^2

Therefore, you can look at the AVC matrix to obtain se[k] and you can calculate S-estimates yourself.

For more information, please refer to:
Rose, J.M. and M.C.J. Bliemer (2013) Sample size requirements for stated choice experiments. Transportation, Vol. 40, No. 5, pp. 1021-1041.

Michiel

[nutterzht123]

Thank you very much for your help!