effects coding with limited priors and sample size?

[Louise]

Dear all,

I am currently developing a choice experiment concerning the acceptance of farmers towards bio-based fertilizers, this experiment will be conducted in 7 countries in Europe.

We are planning to start with a orthogonal model for parameter estimation and later change to a D-efficient design.

So my question, can I do effects coding without priors in an orthogonal design? Is it needed/possible to generate a design that is orth and eff as written below?
I don’t have information on the parameters but for some of the model parameters I could estimate the sign of the priors. How can I include that to improve the model, or is it enough to include priors after first testing an orthogonal model?? For example, prior for b2 (no effects coding) has a negative sign. For b3 I have no information on priors. For b4, the priors also have a negative sign.
The model below gives an error “Error: An attribute has the wrong number of levels for dummy or effects coding. 'b' “.

Design
;alts=alt1,alt2, alt3
;rows=13
;orth=seq
;eff = (mnl, d)
;block=2
;model:
U(alt1)=b2*A[0,1,2,3]+b3.effects*B[0,1,2,3]+ b4*C[0,1,2,3]+b5.effects*D[0,1]+ b6.effects* E[0,1]+ b7.effects* F[0,1] /
U(alt2)=b2*A+b3*B+ b4* C+b5 *D+ b6* E+ b7*F/
U(alt3)=b1$

I don’t have information of the parameters but for some of the model parameters I could estimate the sign of the priors. How can I include that to improve the model, or is it enough to include priors after first testing an orthogonal model?? For example, prior for b2 (no effects coding) has a negative sign. For b3 I have no information on priors. For b4, the priors also have a negative sign.

For a D-efficient MNL model, how do I find the sample size N? I consulted the paper of Rose and Bliemer on Sample size requirement for stated choice experiments but that deals only with sample size for MMNL models?

Thank you in advance for your help.

Louise

[johnr]

Hi Louise

The effects and dummy coding syntax works via the parameters as opposed to the attributes. Hence, you need to provide priors for the first L-1 parameters. You don't need to provide the levels however if the levels you are going to show respondents are something other than 0,1,2.. etc. then sometimes it is helpful to do so.

The correct syntax for your case would be:

Design
;alts=alt1,alt2, alt3
;rows=13
;orth=seq
;eff = (mnl, d)
;block=2
;model:
U(alt1)=b2[0]*A[0,1,2,3]
+ b3[0|0|0].effects*B[0,1,2,3]
+ b4[0]*C[0,1,2,3]
+ b5[0].effects*D[0,1]
+ b6[0].effects* E[0,1]
+ b7[0].effects* F[0,1] /
U(alt2)=b2*A+b3*B+ b4* C+b5 *D+ b6* E+ b7*F/
U(alt3)=b1[0]$

If you know the sign, you can use uniform Bayesian priors, for example b2[(u,-1,0)] or for effects coded variables if you know the ordering b3[(u,-1,-0.75)|(u,-0.75,-0.5)|(u,--0.5,-0.25)].effects for example.

In terms of sample size calculations, the process is exactly the same for all models. The original paper we wrote on S-error was for the MNL model back in 2005 however the reviewers rejected the paper on the grounds that they insisted we do it for the MMNL model. The theory remains the same. The t-rat. = beta_k/(s.e._k/sqrt(N_k)). In the MMNL model, the beta can be either the mean or dispersion (stnd dev. or spread) parameter. In the MNL model, there is no dispersion parameter, just the mean. You can re-arrange to put N_k on the LHS. Note it only works if beta_k is non-zero, as the beta ends up in the denominator. Also, this is the theoretical minimum sample size as it assumes that you got the priors right, and not just beta_k - the standard errors come from the AVC matrix which is a function of the design, X, the betas, and the choice probabilities. The choice probabilities depend on the entire utility function, that is, all it requires all betas be correct.

John