Estimation when using dummy coding in efficient design

[Yuanyuan Gu]

Hi,

Suppose we have a design as below:

Design
;alts = alt1, alt2
;rows = 16
;eff = (mnl, d)
;block = 2
;model:
U(alt1) = b1*A[0,1,2,3,4,5,6,7] + b2.dummy[0|0|0]*B[0,1,2,3] + b3.dummy[0|0|0]*C[0,1,2,3] + b4*A*A/
U(alt2) = b1*A + b2*B + b3*C + b4*A*A
$

You can see that the design allows us to estimate the coefficient for both A and A^2. But is it OK not to estimate the coefficient for A^2 in the regression analysis?

Suppose we have another design as below:

Design
;alts = alt1, alt2
;rows = 16
;eff = (mnl, d)
;block = 2
;model:
U(alt1) = b1*A[0,1,2,3,4,5,6,7] + b2.dummy[0|0|0]*B[0,1,2,3] + b3.dummy[0|0|0]*C[0,1,2,3]/
U(alt2) = b1*A + b2*B + b3*C
$

You can see that the design now doesn't inlude A^2 in the utility function. In this case, is it valid to estimate the coefficient for A^2 in the regression analysis?

Thanks,
Yuanyuan

[Michiel Bliemer]

In the first case, leaving A^2 out of the discrete choice analysis (not regression) is not a problem, you may merely loose some efficiency.

In the second case, you may be able to estimate A^2 but not in all cases (there are instances in which this would not work, but this is case specific). So it is best to include it, even though you may not use it in your estimations later.