Coefficient for ASC in unlabelled design (Bayesian)

[djourdain]

Dear All,

We are making a bayesian design with 2 alternatives + one status quo. We want to optimize the D-efficiency of a MNL formulation with a Bayesian formulation.

The code reads as follows:

Design
;alts = alt1*, alt2*, sq
;rows = 12
;eff = (mnl,d,mean)
;bdraws = gauss(2)
;model:
U(alt1) = b2[(n,0.205013,0.104599)] * wetcon[3,6,12] +
b3[(n,0.230640,0.117673)] * infedu[8,12,16] +
b4[(n,0.283864,0.144829)] * toupre[1,2.5,5,7.5] +
b5[-0.030752] * hhtax[0,10,20,40,80,120] /

U(alt2) = b2 * wetcon +
b3 * infedu +
b4 * toupre +
b5 * hhtax /

U(sq) = b1[(n,-0.030752,0.015)] +
b2 * sqw[3] +
b3 * sqi[12] +
b4 * sqt[2.5] +
b5 * sqta[0]
$


By doing so, I have a fairly good efficiency, but have some troubles with balancing utilities (at least for a few cases).
I also noticed that the b1 coefficients did not seem to be taken care of in the results (so I guess in the calculations?)
Here are the top of the results:

MNL efficiency measures

Fixed Bayesian mean
D error 0.005656 0.006901
A error 0.019381 0.02364
B estimate 57.257352 0.440073
S estimate 1.722874 7.264018

Prior b2 b3 b4 b5
Fixed prior value 0.205013 0.23064 0.283864 -0.030752
Sp estimates 1.679315 1.642653 1.722874 1.086431
Sp t-ratios 1.512481 1.529267 1.493239 1.88042
Sb mean estimates 4.228112 4.353352 4.743862 1.207923
Sb mean t-ratios 1.392477 1.332263 1.338539 1.785793

Puzzled by the fact that b1 was presented in the results, I opted for a slightly different formulation, where I multiply b1 by a ASC attribute.
Here is the second formulation:

Design

;alts = alt1*, alt2*, sq
;rows = 12
;eff = (mnl,d,mean)
;bdraws = gauss(2)


;model:

U(alt1) = b2[(n,0.205013,0.104599)] * wetcon[3,6,12] +
b3[(n,0.230640,0.117673)] * infedu[8,12,16] +
b4[(n,0.283864,0.144829)] * toupre[1,2.5,5,7.5] +
b5[-0.030752] * hhtax[0,10,20,40,80,120] /

U(alt2) = b2 * wetcon +
b3 * infedu +
b4 * toupre +
b5 * hhtax /

U(sq) = b1[(n,-0.030752,0.015)] * ASC[1] +
b2 * sqw[3] +
b3 * sqi[12] +
b4 * sqt[2.5] +
b5 * sqta[0]
$

The model is running fine as well, and results are taking care of b1. However, I noticed that it inflates sharply the S-error (mainly due to the b1 coefficient).
Here are the results:

Fixed Bayesian mean
D error 0.013827 0.016186
A error 0.170227 0.196376
B estimate 53.945417 0.44913
S estimate 3138.554963 7669.646053

Prior b2 b3 b4 b5 b1
Fixed prior value 0.205013 0.23064 0.283864 -0.030752 -0.030752
Sp estimates 1.602985 1.762341 1.732299 0.985074 3138.554963
Sp t-ratios 1.548073 1.476424 1.489171 1.974793 0.034986
Sb mean estimates 4.241651 4.338935 4.374616 1.173676 7669.646053
Sb mean t-ratios 1.360615 1.32033 1.308121 1.812575 0.033181

Two questions to the forum:
1. Which of the two formulations is correct ?
2. If the second one is the only correct one, I do not understant why the S-error is becoming so large for this coefficient?

Thank you in advance for your comments and advices,

Best,

Damien

[Michiel Bliemer]

The first syntax is the proper way to add constants. The reason why Ngene does not report results for b1 is because Ngene by default does not optimise for estimating constants. Ngene DOES take the ASC into account when calculating utilities and calculates the Fisher information matrix and covariance matrix including b1, but when calculating the D-error it ignores b1. If you believe that optimising on the ASC is important then you need to add the command ;con to your syntax, and Ngene will then report results for b1.

Note that your ASC (b1) is very small (it has a marginal effect on the utility of SQ), which is the reason why the S-estimate for b1 is very large. It may well be that the constant in the SQ alternative in model estimation turns out to be not statistically significant (i.e. b1 could be considered zero), which is a result that is not entirely unexpected (b1 represents the utility for the label "status quo" and this label does not necessarily affect choice behaviour). Therefore, I would recommend not adding ;con to your syntax.

Michiel

[djourdain]

Dear Michiel,

Thank you for this answer and advise

Damien