Model to choose from pilot test for priors

[dce.farmers]

Dear choice modelers,

I have been collecting data for my pilot test with 25 respondents and I would like to extract priors to estimate an efficient Bayesian design for the final data collection.

I am a bit unsure which model I should keep to extract my priors from. Below, the first model without any interaction term between my COST attribute (continious variable) and one level of my categorical attribute. The second model is without this interaction term. They were both estimated with a conditional logit. I noticed that the SE for the coefficient of the level of of my categorical attribute TVXINDGP increases a lot once I control for this interaction term. I originally had this interaction term in my Ngene design for the pilot test as it makes sense theoretically so I would prefer to keep it. Should I however exclude it here as it creates large SE for one of my level attribute of interest or is it not a problem to exact priors with large SE and keep model 2?

Thanks a lot in advance for the help!
Best,
Gaëlle

Model 1 (without interaction term):

-----------------------------------------------------------------------------
Discrete choice (multinomial logit) model
Dependent variable Choice
Log likelihood function -143.43119
Estimation based on N = 150, K = 9
Inf.Cr.AIC = 304.9 AIC/N = 2.032
---------------------------------------
Log likelihood R-sqrd R2Adj
Constants only -153.8090 .0675 .0386
Note: R-sqrd = 1 - logL/Logl(constants)
Warning: Model does not contain a full
set of ASCs. R-sqrd is problematic. Use
model setup with ;RHS=one to get LogL0.
---------------------------------------
Response data are given as ind. choices
Number of obs.= 150, skipped 0 obs
--------+--------------------------------------------------------------------
| Standard Prob. 95% Confidence
CHOICE| Coefficient Error z |z|>Z* Interval
--------+--------------------------------------------------------------------
Constant| -2.54999* 1.51495 -1.68 .0923 -5.51924 .41926
SUPPINDI| .24805 .29113 .85 .3942 -.32255 .81865
SUPPCOL| .47318* .27365 1.73 .0838 -.06316 1.00953
COST|-.32438D-04 .2676D-04 -1.21 .2254 -.84887D-04 .20011D-04
TVXINDGP| .11983 .31365 .38 .7024 -.49491 .73456
TVXCOOP| -.05282 .32303 -.16 .8701 -.68595 .58031
PULVINGP| -.77889*** .26387 -2.95 .0032 -1.29607 -.26172
PULVCOOP| -.65234** .28022 -2.33 .0199 -1.20156 -.10312
TECHCOLL| .38821* .21276 1.82 .0681 -.02879 .80520
--------+--------------------------------------------------------------------
nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx.
***, **, * ==> Significance at 1%, 5%, 10% level.
Model was estimated on Apr 03, 2024 at 00:38:02 PM
-----------------------------------------------------------------------------


Modèle 2 (with interaction term):
-----------------------------------------------------------------------------
Discrete choice (multinomial logit) model
Dependent variable Choice
Log likelihood function -143.37839
Estimation based on N = 150, K = 10
Inf.Cr.AIC = 306.8 AIC/N = 2.045
---------------------------------------
Log likelihood R-sqrd R2Adj
Constants only -153.8090 .0678 .0357
Note: R-sqrd = 1 - logL/Logl(constants)
Warning: Model does not contain a full
set of ASCs. R-sqrd is problematic. Use
model setup with ;RHS=one to get LogL0.
---------------------------------------
Response data are given as ind. choices
Number of obs.= 150, skipped 0 obs
--------+--------------------------------------------------------------------
| Standard Prob. 95% Confidence
CHOICE| Coefficient Error z |z|>Z* Interval
--------+--------------------------------------------------------------------
Constant| -2.15633 1.94088 -1.11 .2666 -5.96038 1.64772
SUPPINDI| .24568 .29068 .85 .3980 -.32404 .81540
SUPPCOL| .47685* .27420 1.74 .0820 -.06058 1.01428
COST|-.25181D-04 .3490D-04 -.72 .4705 -.93576D-04 .43214D-04
TVXINDGP| 1.28301 3.59360 .36 .7211 -5.76032 8.32635
TVXCOOP| -.01094 .34721 -.03 .9749 -.69146 .66957
PULVINGP| -.78189*** .26400 -2.96 .0031 -1.29932 -.26446
PULVCOOP| -.65822** .28113 -2.34 .0192 -1.20923 -.10722
TECHCOLL| .37381* .21773 1.72 .0860 -.05293 .80055
COST_TVI|-.22903D-04 .7049D-04 -.32 .7452 -.16105D-03 .11525D-03
--------+--------------------------------------------------------------------
nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx.
***, **, * ==> Significance at 1%, 5%, 10% level.
Model was estimated on Apr 03, 2024 at 00:40:59 PM
-----------------------------------------------------------------------------

[Michiel Bliemer]

You do not necessarily have to choose, you can optimise on both models at the same time, e.g.

;eff = 2*model1(mnl,d,median) + 1*model2(mnl,d,median)
;model(model1): ? without interaction term
...
;model(model2): ? with interaction term
...

A large standard error could cause issues because of extreme values drawn from the distribution, so in that case I would use median instead of mean for Bayesian efficiency and you could also decide to manually reduce the standard deviation of the normally distributed coefficient.

Michiel