Using parameter estimates from simulated model as priors

[tn73]

Hi Team,
I have conducted a pilot survey and used the data collected to estimate a model. I have then used the parameter estimates from the pilot as priors in an experimental design for my final survey. I have also simulated the design (estimated the deterministic components of utility and the random components and assumed that the alternative with the highest utility is selected in each choice situation using a virtual sample of 200). All the parameter estimates for the simulated model are highly significant with the expected signs. Further, I have used the parameter estimates from the simulated model as priors in generating a new design which has a lower D-Error and smaller minimum sample requirement and I am tempted to use this in my final survey. My question is "Is it theoretically correct to use the more efficient design based on results from the simulated model in my final survey?"

Regards
tn73

[Michiel Bliemer]

I assume you have simulated the data using the parameter estimates from the pilot study? And then you estimated the model based ont he simulated data. If you would have used a large enough sample (perhaps 200 is not enough) then you should have obtained exactly the parameter estimates that you put in as priors. If not, then your sample size was not large enough. McFadden proved that the logit model will provide unbiased estimates independent of the design you use, so you should always retrieve the parameters that you put into the simulation after estimation. This is asymptotic behaviour, so large sample sizes. So you can just use the priors you obtained from the pilot study and it is not necessary to simulate data as the equations in Ngene make use of the asymptotic properties of the logit model. The reason that you obtain lower D-errors is because you have used different priors. You can only compare designs based on the same priors. You can try to use larger sample sizes (e.g., 1000 or 10000) and you should retrieve the prior parameter estimates. Note that the standard errors (and therefore also the D-error) are by default all asymptotic values.