S estimate result from Bayesian efficient design

[sukunta]

Dear Michiel Bliemer,
I run the syntax

Code: Select all

design
;alts=alt1*,alt2*,alt3
;rows=12
;block=2
;eff =(mnl,d,mean)
;con
;bdraws = gauss(3)
;model:
U(alt1)=b0 [(n, 2.501704, 1.141856)]+b1.dummy[(n,-0.5077506, 0.2668998)]*private[1,0]+b2.dummy[(n,0.4270188, 0.1971011)]*open[1,0]+b3[(n, 0.0121578, 0.0109568)]*time[10,20,30]+ b4.dummy[(n, 1.035963, 0.3080124) |(n, 0.740783, 0.2492737)]*channel[1,2,0]/
U(alt2)= b0 [(n, 2.501704, 1.141856)]+b1* private +b2* open +b3* time +b4* channel
$

The result of Sp estimate result show

Code: Select all

                  
   Fixed   Bayesian mean            
D error   0.293706   0.315347            
A error   1.508035   2.351372            
B estimate   10.084915   0.154285            
S estimate   39.027675   208.997944            
                  
Prior   b0   b1(d0)   b2(d0)   b3   b4(d0)   b4(d1)
Fixed prior value   2.501704   -0.5077506   0.4270188   0.0121578   1.035963   0.740783
Sp estimates   3.802113   7.143694   8.902911   39.027675   3.721982   6.375459
Sp t-ratios   1.005179   0.733322   0.656886   0.31374   1.015942   0.776248
Sb mean estimates   9.476788   147.107181   43.784163   50.330443   5.3621   11.120955
Sb mean t-ratios   0.850047   0.69559   0.629299   0.358837   0.974996   0.748274


How to interprete the sample siaze for this model?
Sincerely yours,
Sukunta

[Michiel Bliemer]

It means that if the parameter estimates turn out to be equal to the mean, then b3 is the most difficult parameter to estimate, requiring at least 61 respondents to estimate this parameter with a t-ratio of more than 1.96. The reason that this parameter is difficult to estimate is because time makes a very small contribution to utility, only around 0.1, i.e., if these priors are correct, time does not really matter much in choice. To estimate all parameters with a t-ratio of 1.96 or higher, you would therefore need at least 61 respondents.

Taking unreliability about the priors into account, b1(d0) is the most difficult to estimate parameter (on average), mainly because it has a large unreliability and can attain small values (which are hard to estimate). On average, over the assumed distribution, 147 respondents are needed. The overall S-estimate for all parameters is 209 respondents, which is computed as E[max(S_k)], where E is the expectation, and S_k is the sample size estimate for parameter k. This means that for some draws in the distribution, you may need a quite large sample size. Your prior distributions are quite wide so if the true parameters turn out to be extreme values of the distribution then a large sample size may be required.

Michiel

[sukunta]

Dear Michiel Bliemer,
Thank you so much. Please, explain some points to me as follow,
1.I don't know where is the number of b3 proposed in the result that requiring at least 61 respondents?
2.What is the sample size I should select (147 and 209)?
3.The model is blocked with 2, then I should double the sample size from Ngene suggestion or not?

Sincerely yours,
Sukunta

[Michiel Bliemer]

1. Sorry 61 came from the Ngene run that I did, it should be 39 in your case.
2. 209 at minimum, you may want to go much larger since a t-ratio of 1.96 is not much, if you want reliable parameter estimates you need much more. Most of my surveys have sample sizes of 500-1000 or more.
3. Yes then you need to double the sample size.

Michiel

[sukunta]

Dear Michiel Bliemer,
Thank you so much. If I have 200 of the sample, could the parameters of the model be estimated?

Sincerely your,
Sukunta

[Michiel Bliemer]

That is not possible to say in advance given that priors are only best guesses. Sample size estimates should only be used as a rough guidance... so whether it is 50, 500 or 5000. Sample sizes are in many cases determined by budget. Based on your sample size estimates, it is likely that they will all be statistically significant, but if your priors are far from the actual parameter values then they may be (much) lower or higher.

[sukunta]

Dear Michiel Bliemer,
Thank you so much for your kindness.
Sincelery yours,
Sukunta