I have a question about the efficient design with Bayesian priors.
In this case I have to include mean and st. deviations for the priors.
I first did a pre-test, and estimated MNL model (in NLogit).
In order to create the efficient design with Bayesian priors, I will use the mean values obtained from the estimates of the MNL model.
Which values do you recommend that I use for the st. deviations of the priors?
Thanks,
Efficient design with Bayesian priors
Moderators: Andrew Collins, Michiel Bliemer, johnr
Re: Efficient design with Bayesian priors
Hi Ellenvl
There is no right or wrong answer to this question. The use of Bayesian priors represents the degree of uncertainty you as an analyst has with regards to the true population level estimates. The greater your uncertainty, the greater the std deviations you will use.
One trick that Michiel and I have used in the past which seemed to work well was to use the std errors from the pilot as the std dev.s in the Bayesian design. I'm not saying that this is the only strategy, but as I said, it seems to work well for us.
John
There is no right or wrong answer to this question. The use of Bayesian priors represents the degree of uncertainty you as an analyst has with regards to the true population level estimates. The greater your uncertainty, the greater the std deviations you will use.
One trick that Michiel and I have used in the past which seemed to work well was to use the std errors from the pilot as the std dev.s in the Bayesian design. I'm not saying that this is the only strategy, but as I said, it seems to work well for us.
John
Re: Efficient design with Bayesian priors
thanks for your reply!
I appreciate it!
I appreciate it!
Re: Efficient design with Bayesian priors
Hi Ellenvl
No probs. You need to think of this from a Bayesian perspective. The priors in this case represent the degree of uncertainty you the analyst has as to the true estimate. If you assume a Normal distribution, then you placing a greater part of the density near the mean, and it tapers off around this value. If you assume a uniform distribution, then you are assuming an equal probability for each point in the uniform space.
Hence if you adopt the approach I mentioned previously, you are basically saying that the most likely population estimate is the mean derived from the pilot estimates, and your level of uncertainty around this mean estimate is defined from the standard error obtained from the pilot. This may or may not be a good value to assume as it depends on how much faith you are willing to place on the pilot. One reason we do this however is that the standard error is linked to the sample size (of your pilot), with smaller sample sizes giving larger standard errors meaning you have less certainty. As the pilot sample increases in size, the estimates should approach the true population estimates. In reality, what we are really doing is borrowing a bit from the Bayesian camp and a bit from the classical camp in doing this. We probably will get kicked out of both camps when they find out as both can be quite feral sometimes. So I won't tell them if you don't.
John
No probs. You need to think of this from a Bayesian perspective. The priors in this case represent the degree of uncertainty you the analyst has as to the true estimate. If you assume a Normal distribution, then you placing a greater part of the density near the mean, and it tapers off around this value. If you assume a uniform distribution, then you are assuming an equal probability for each point in the uniform space.
Hence if you adopt the approach I mentioned previously, you are basically saying that the most likely population estimate is the mean derived from the pilot estimates, and your level of uncertainty around this mean estimate is defined from the standard error obtained from the pilot. This may or may not be a good value to assume as it depends on how much faith you are willing to place on the pilot. One reason we do this however is that the standard error is linked to the sample size (of your pilot), with smaller sample sizes giving larger standard errors meaning you have less certainty. As the pilot sample increases in size, the estimates should approach the true population estimates. In reality, what we are really doing is borrowing a bit from the Bayesian camp and a bit from the classical camp in doing this. We probably will get kicked out of both camps when they find out as both can be quite feral sometimes. So I won't tell them if you don't.
John