## pilot study

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### pilot study

Dear Professor Bliemer,

I would like to ask questions for the development of the research after a pilot study.

A pilot study was carried out in order to obtain prior values.

The significant parameters were only those related to Confort_TP and Cost_TP.
All parameters had the correct (expected) signal, with the exception of Time_RD.

A Bayesian design was used to generate a final design for the study. Is the procedure correct in syntax or do you suggest any correction? How can I handle parameters with unexpected signal?

Code: Select all
`design;alts = TP,RD;rows =12;block =2;eff = (mnl,d,median);cond:if (RD.Cost_RD = 3, RD.Time_RD <> 15),if (TP.Cost_TP=4.80 and TP.Time_TP = 18 and RD.Cost_RD =3, RD.Time_RD <>10) ;model:U(TP) = b0[(n,0.407,0.593)]  + b1_TP[(n,0.72,0.317)]* Confort_TP[0,1]+ b2_TP[(n,-0.286,0.113)]* Cost_TP[2,4.80] + b3_TP[(n,-0.004,0.019)] * Time_TP[13,18] /U(RD) =                                                               b2_UBER[(n,-0.005,0.038)]*Cost_RD[3,5] + b3_RD[(n,0.013,0.031)]*Time_RD[10,15]\$`

Unfortunately, the pilot survey had a small sample and had to be closed due to time constraints for the survey.
Thank you for your attention.
Regards,
Felipe
felipelobo

Posts: 11
Joined: Sat Sep 05, 2020 1:17 am

### Re: pilot study

The syntax looks fine.

For coefficients with unexpected sign you could set the mean to zero, i.e., [(n,0,...)] or you could use a uniform distribution forcing the draws to be on the correct sign, for example for a negative sign [(u,-1,0)] where -1 and 0 are the lower and upper bounds respectively, where you want to choose these bounds such that the resulting standard deviation in the uniform distribution somewhat matches the standard error of the parameter estimate. Note that this is all very much an art and not an exact science.

Michiel
Michiel Bliemer

Posts: 971
Joined: Tue Mar 31, 2009 4:13 pm

### Re: pilot study

Dear Professor Bliemer,

Thank you for your answer. We adopted a small pilot study avoiding prior values from literature.

One last doubt regarding the design generated with this syntax was the high number of S estimate.

Is the high value of the S estimate a problem for the final design? Could this cause a problem for estimation in the study later?

Thank you for your attention.
Regards,
Felipe
felipelobo

Posts: 11
Joined: Sat Sep 05, 2020 1:17 am

### Re: pilot study

High S-estimates are due to very small priors, likely due to insufficienty sample size used in your pilot study.;

For example, b2_TP = -0.286 while b2_UBER = 0.005. The latter is very small, resulting in extrenely high sample size estimates because your prior tells your essentially that cost for UBER does not matter. But it is more likely that b2_TP is similar to b2_UBER. So with a limited sample size, I would have estimated generic coefficients b2 and b3, and then use the parameter estimate for b2 as a prior for both b2_TP and b2_UBER, and the parameter estimate for b3 as a prior for both Time_TP and Time_RD. That way, your parameter estimates become more robust while you are still designing your experiment for alternative-specific coefficients.

Michiel
Michiel Bliemer

Posts: 971
Joined: Tue Mar 31, 2009 4:13 pm

### Re: pilot study

Dear Professor Bliemer,

I estimated the MNL model for the generic coefficients as you indicated in the last post.

All coefficients were significant with the exception of comfort. In Ngene, I developed the design with the syntax below.

Code: Select all
`design;alts = TP,RD;rows =12;block =2;eff = (mnl,d,mean);cond:if (RD.Cost_RD = 3, RD.Time_RD <> 15),if (TP.Cost_TP=4.80 and TP.Time_TP = 18 and RD.Cost_RD =3, RD.Time_RD <>10) ;model:U(TP) = b0[(n,-0.7734,0.3351)]  + b1_TP[(n,0.5604,0.3174)]* Comfort_TP[0,1]+ b2_TP[(n,-0.0805,0.0276)]* Cost_TP[2,4.80] + b3_TP[(n,-0.0626,0.0234)] * Time_TP[13,18] /U(RD) =                                                               b2_RD[(n,-0.0805,0.0276)]* Cost_RD[3,5] + b3_RD[(n,-0.0626,0.0234)]* Time_RD[10,15]\$`

The result obtained S estimate Fixed (357) lower than the value obtained with non-generic coefficients.

For the final study that will be applied with this design, we intend to estimate non-generic coefficients. Is there a problem with adopting generic coefficients in this way as it was used for both alternatives?

Thank you for your attention.
Regards,
Feliipe Souza
felipelobo

Posts: 11
Joined: Sat Sep 05, 2020 1:17 am

### Re: pilot study

No there is no problem, you are optimising your design for alternative-specific coefficients, namely you have specified b2_TP and b2_RD, i.e. Ngene assumes that you are estimating two different coefficients. All you have done is assuming the same 'best guesses' (priors) for the two parameters because your limited pilot sample size was not enough to estimate them reliably separately. But your design is now optimised for the same model as previously, namely with alternative-specific coefficients.

Michiel
Michiel Bliemer

Posts: 971
Joined: Tue Mar 31, 2009 4:13 pm