Beginner: help with bayesian design (priors, s-estimate)

[miles]

Dear moderators,

I'm a beginner in Ngene and am hoping to ask for help with the best approach for the following.

Context:
We conducted a pilot study (sample size =54) to obtain priors to be used for our main DCE study. We have used these priors in our design and have run it, however, upon looking at our S-estimate, we are seeing a need for a very big sample size.

We got very large “Sb mean estimates” for 3 priors (b1(e2), b2 (e0), b3 (e0)). Pilot results indicate that these are non-significant findings in the analysis.

Could we possibly receive guidance on what we could do to potentially get a more reasonable S-estimate? As well as receive feedback on anything else we could be doing for the design.

Code: Select all

Design
? Bayesian D-efficient Design

;alts = alt1*, alt2*,none
;rows = 30
;block = 3
;eff = (mnl,d,mean)
;bdraws = gauss(2)
;alg = mfederov
;con

;model:
U(alt1) =
          b1.effects[(n,0.63380,0.12606)|(n,-0.41652,0.14772)|(n,-0.13683,0.14196)|(n,0.70567,0.12576)]  *  modality[2,3,4,5,1]
        + b2.effects[(n,0.12632,0.09209)|(n,0.25889,0.09091)]                                            *  timing[2,3,1]
        + b3.effects[(n,0.07167,0.08963)|(n,-0.00446,0.09256)]                                           *  content[2,3,1]
        + b4.effects[(n,0.38940,0.06343)]                                                                *  interactivity[2,1]

/

U(alt2) =
          b1.effects * modality
        + b2.effects * timing
        + b3.effects * content
        + b4.effects * interactivity

/

U(none) = asc[0.38949]

$

These are the estimates we got after running for over a day:

Code: Select all

               Fixed      Bayesian mean                     
D error        0.161077   0.163281                        
A error        0.208272   0.211634                        
B estimate     84.59024   0.821264                        
S estimate     24894.86   24085.36                        
                              
Prior                  b1(e0)     b1(e1)     b1(e2)     b1(e3)     b2(e0)     b2(e1)     b3(e0)     b3(e1)     b4(e0)     asc
Fixed prior value      0.6338    -0.41652   -0.13683    0.70567    0.12632    0.25889    0.07167   -0.00446    0.3894     0.38949
Sp estimates           2.828645   8.077462   68.55179   2.386854   32.14918   7.400741   101.0989   24894.86   2.060537   4.320029
Sp t-ratios            1.165378   0.689634   0.236726   1.268654   0.345677   0.720474   0.194932   0.012422   1.365419   0.943002
Sb mean estimates      3.248376   11.62297   23614.08   2.673294   229.2686   10.96873   841.891    58.93372   2.246908   4.396148
Sb mean t-ratios       1.157161   0.676964   0.238202   1.259272   0.344044   0.715282   0.243898   0.255867   1.352993   0.934983

Thank you and looking forward to your thoughts and feedback.

[Michiel Bliemer]

The sample size estimates for some of the effects coded coefficients are large because the priors are very close to zero and therefore you may not be able to estimate them to be statistically significant to zero. However, with effects coding you would generally test hypotheses of deviation from the mean instead of deviation from zero, so in that case the sample size estimates would be different.

If you intend to look at statistical significant with deviations from zero, i.e., deviations from the base level in your categorical attributes, then I would suggest you use dummy coding. With dummy coding all parameters will be larger, i.e., further away from zero, and will be much easier to estimate. So perhaps just estimate everything with dummy coding and have another look at your sample size estimates.

Michiel