examining both linear and non-linear effects of the same att

[gilbiiro]

I will like to examine both the linear and non-linear effects of a particular attribute. Do I have to first enter a parameter (B) for the attribute without a dummy/effects coded to examine the linear component and then enter it again as a dummy/effect coded in the same model within the Ngene syntax to examine the non-linear effects? See my Ngene syntax below
Design
;alts = alt1, alt2, alt3
;rows =18
;eff = (mnl,d)
;block = 3
;reject:
Alt1.C= Alt1.D,
Alt1.C= Alt1.F,
Alt1.D=0, Alt1.F=2,
Alt1.F=0, Alt1.D=2,
Alt2.C= Alt2.D,
Alt2.C= Alt2.F,
Alt2.D=0, Alt2.F=2,
Alt2.F=0, Alt2.D=2

;model:
U(alt1)= b1[0] + b2[0]* A[0,1,2] + b3[0]* B[0,1,2]+ b4[0]* C[0,1,2]+ b5[0]* D[0,1,2] + b6[0]* E[0,1,2]+ b7[0]* F[0,1,2]+ b8[0]*C*D + b9[0]*C*E+ b10[0]*C*F +b11[0]*D*F+ b12[0]*A*F +b2.effects* A[0,1,2] + b3.effects* B[0,1,2]+ b4.effects* C[0,1,2]+ b5.effects* D[0,1,2] + b6.effects* E[0,1,2]+ b7.effects* F.[0,1,2] /

U(alt2)= b2* A + b3* B + b4* C + b5* D + b6* E + b7* F + b8*C*D + b9*C*E+ b10*C*F +b11*D*F+ b12*A*F +b2.effects* A[0,1,2] + b3.effects* B[0,1,2]+ b4.effects* C[0,1,2]+ b5.effects* D[0,1,2] + b6.effects* E[0,1,2]+ b7.effects* F.[0,1,2] $

i will appreciate your comments on my design. I am doing a pilot to generate prior parameters for the final D-efficient design



Best regards,
Gilbert

[Michiel Bliemer]

The utility functions that you specify need to be the functions of the model that you are most likely to estimate.
If you think you will estimate non-linear effects, then only include dummy/effects coded parameters, you cannot include the same attribute/parameter twice. If you are unsure about linear or non-linear effects, then it is best to choose the dummy/effects coded specification, as the linear effects is merely a special case. So I would suggest you keep b2.effects and remove b2.

Alternatively, you could specify two different models, one model (M1) with linear effects, and another one (M2) with non-linear effects. You would then specify ;model(M1): and ;model(M2), please refer to the Model Averaging section in the Ngene manual. In that case, you could optimise a design that is efficient for estimating both models.

[gilbiiro]

Thank you very much Michiel for this. I am very grateful.

Regards,
Gilbert

[gilbiiro]

In an attempt to design a very efficient DCE design using Ngene; I completed a pilot study with 49 respondents and have analyzed the data to derive prior parameters for my final DCE design. However, most of the parameters are insignificant and one (insurance premium) strangely has a positive sign (though from the literature it is expected to be negative). I don’t know if it is because the model I used for design of the pilot study was not efficient or because the sample size was small? Could the positive sign of the premium be an indication of the fact that the attribute levels of the premium are a bit low (in the pilot some respondents actually said the figures were too low while others said they were just ok). These figures were derived from FGDs, six months ago.
I am afraid that if I use these results of the pilot to define prior parameters for my design, I may end up wrongly estimating the through effects of the attributes and levels. Can I just ignore the prior parameters and assume zero priors for my design? What will be the advantages of using the parameters from the pilot ( I am not sure of ) over that of assuming zero priors?
I have however, learnt a lot from the pilot that will help me ensure that I maximize respondents efficiency in my study.
Thanks for your usual support
Gilbert

[Michiel Bliemer]

The sample size could indeed be too small, in particular if you have a lot of dummy and effects coded variables, as they typically need a larger sample size. It could also be that your attribute level range is very narrow (i.e. $1-$2 is a narrow range, while $0-$100 is a wide range for a cost attribute). The wider the range, the more information you collect about trade-offs in your design, and the easier it becomes to obtain statistically significant parameter estimates. I cannot really say much about the parameter with unexpected sign, there can be several reasons that are specific to each experiment.

There are several benefits in using non-zero priors. The closer you are to the true values, the more efficient your design will be. So by setting them equal to 0, you state that you do not even know the sign. When do you not put the sign of the parameters in, Ngene can also not assess whether a certain alternative in the choice task is dominant or not. It is always important to avoid any dominant alternatives (i.e., alternatives with attribute levels that are such that they are all 'better' than the attribute levels of the other alternatives; for example route A with 10 minutes travel time and $1 cost, and route B with 15 minutes travel time and $2, clearly route A is dominant, which will have severe impacts on your model results and should be avoided at all times).

So which values to choose. You could opt to include the values you obtained from your estimates, even though they may not be significant. At least they have the correct sign (and you probably want to adjust the sign of that single parameter). The parameters are likely small. If you are a bit hesitant in using these values directly, you can choose to go for a value that is in between 0 and the estimated parameter value, so a bit more conservative. Setting the priors for example to half the estimated values will likely ensure that the true value is closer to this value than to zero. Hence, the design will be more efficient than with using zero priors. Since you are quite uncertain about the priors, it is good to use Bayesian priors (see Ngene manual) by defining the uncertainty you have about the prior.

Once you have set non-zero priors, so all parameters have a sign, Ngene can rule out dominant alternatives in the design. In order to do this, you have to put a * after each name for each unlabelled alternative, so:

;alts = alt1*, alt2*, alt3

Further, you need to set the correct attribute levels. Now you have used 0,1,2, but you will need to put in the actual attribute levels that you will use for estimation. Of course for dummy/effects coded parameters, you can just put in [0,1,2], but please note that the last attribute level is the base when you define the priors.

[gilbiiro]

Thank you very much Michiel. I will try implementing your recommendations and if there any concerns, i will get back to you.

[gilbiiro]

I have finally settled on the following design for my main study. However, the best D-error I can get for my design is 0.27. Is this design efficient? If this is not good what can I do to improve upon the efficiency? The priors are mainly from my pilot

Syntax

Design
;alts = alt1*, alt2*, alt3
;rows =18
;eff = (mnl,d)
;block = 3

;Model:
U(alt1)= b1[-2.95] + b2.effects[0.35|0.36] * A[0,1,2] + b3.effects[0.22|0.27]* B[0,1,2]+ b4.effects[1.79|0.81]* C[0,1,2]+ b5.effects[0.92|0.78]* D[0,1,2] + b6.effects[1.80|1.40] * E[0,1,2]+ b7[-0.04] *F[0,1,2]/

U(alt2)= b2.effects [0.35|0.36] * A + b3.effects[0.22|0.27]* B + b4.effects[1.79|0.81] * C + b5.effects [0.92|0.78] * D + b6.effects [1.80|1.40] * E + b7 [-0.04] * F

MNL efficiency measures obtained
D error 0.272077
A error 0.531492
B estimate 44.471383
S estimate 215.499891
D optimality 64.016749% Evaluation: 165420