Generating and Evaluating the Designs

[bye1830]

Dear Ngene team,

While I have been generating choice experiment designs using Ngene, I have many questions that I hope someone can help with. Thank you in advance for your time and help.

In my current design, there are three labelled alternatives (a battery electric truck, a hydrogen truck, and a diesel truck as a status quo alternative) and the following seven attributes, each with their specific attribute levels:

• Purchase costs
• Operating costs
• Driving range 
• Emissions
• Shortest distance to an off-site fueling/charging station
• On-site infrastructure construction costs
• Refueling/charging time

Among these attributes, some are with a single-level for each alternative. For example, the "emissions" is 0% for battery electric and hydrogen options and 100% for diesel option without any variations. When I include these single-level attributes in the utility specification, I found that Ngene could not generate an efficient design. Once I remove these single-level attributes, it worked. So, my first questions is:

Q1. Typically, should an attribute with a single level be excluded from the utility specification?

My second question is about orthogonal designs. While I was able to generate efficient designs, Ngene couldn't generate an orthogonal design with an error message saying "Warning: One or more attributes will not have level balance with the number of rows specified: bev.pcostz, bev.offsitez, hfcev.pcostz, hfcev.ocosth, hfcev.rangeh, hfcev.offsitez. [Orthog] No design found." Here is the code that I used.

Code: Select all

Design
? orthogonal sequential
;alts = BEV, HFCEV, DSL
;rows = 40
;orth = seq2
;model:
U(BEV) = b1 +
         b2*pcostz[105,110,115,125,150,175,200] +
         b3*ocostb[50,70] +
         b4*rangeb[100,200,300,500] +
         b5*offsitez[10,20,60] +
         b6*onsiteb[0,25,50,75,100] /

U(HFCEV)= b7 +
         b2*pcostz +
         b3*ocosth[90,115,130] +
         b4*rangeh[300,500,700] +
         b5*offsitez +
         b6*onsiteh[0,25,50,75,100] /

U(DSL) = b2*pcostd[100] +
         b3*ocostd[100] +
         b4*ranged[700] +
         b5*offsited[5] 								
$

Q2. So, I wonder if the certain numbers of attribute levels in this experiment would inherently cause level unbalance and lead to the failure of generating orthogonal design. Do you happen to know about the reasons of the failure? Also, are there any ways to correct this code?

The next two questions are about efficient design. I tried zero priors, fixed priors, and random priors. For fixed and random priors, I set their values and distributions based on some assumptions while there is very limited knowledge in literature. Here's an example of the code that I used for an efficient design.

Code: Select all

Design
? efficient design 
;alts = BEV, HFCEV, DSL
;rows = 40
;block = 5
;eff = (mnl, d)
;rdraws = halton(200)
;alg = swap (stop = total(10100 iterations))
;model:
U(BEV) = b1[n, 0.4800, 0.1600] +
         b2[n, -0.0300, 0.0100]*pcostz[105,110,115,125,150,175,200] +
         b3[n, -0.0800, 0.0267]*ocostb[50,70] +
         b4[n, 0.0120, 0.0040]*rangeb[100,200,300,500] +
         b5[n, -0.0700, 0.0233]*offsitez[10,20,60] +
         b6[n, -0.0700, 0.0233]*onsiteb[0,25,50,75,100] /

U(HFCEV)= b7[n, 1.4500, 0.5000] +
         b2*pcostz +
         b3*ocosth[90,115,130] +
         b4*rangeh[300,500,700] +
         b5*offsitez +
         b6[n, -0.0700, 0.0233]*onsiteh[0,25,50,75,100] /

U(DSL) = b2*pcostd[100] +
         b3*ocostd[100] +
         b4*ranged[700] +
         b5*offsited[5] 								
$

And, here is a summary of resulted statistical efficiencies across different prior settings.

• Types ............ | D-error | A-error | B-estimate | S-estimate
  ------------------------------------------------------------------------------
  Zero prior .......| 3.20E-05 | 7.50E-05 | 100 | 0
  Fixed prior ......| 4.37E-04 | 1.24E-03 | 3.276 | 1.562
  Random prior A | 4.36E-04 | 1.23E-03 | 2.955 | 1.552
  Random prior B | 1.36E-04 | 9.15E-04 | 18.549 | 0.667

Q3. D-errors and A-errors look quite small for all these prior settings. When comparing the random prior types A and B, I wonder how meaningful is an improvement of D-error from 0.0000436 to 0.0000136?

Q4. (In the case of efficiencies being just comparable between different prior settings) Aside from D-error, A-error, B-estimate, and S-estimate, are there any other things to consider when selecting a final design?

Meanwhile, I feel unsure about these prior assumptions although I discussed this with other researchers. There is too limited literature in this area. I might then need to do a pilot survey to obtain more reliable priors. So, the next two questions are about a pilot survey.

Q5. I'd expect around 50 to 100 responses for a full survey at best, given an unpromising response rate in this study area. Then, how many responses should be targeted for a pilot survey?

Q6. For a pilot survey, which design would be better to be used, between zero prior vs. fixed prior vs. random prior vs. orthogonal?

Now, I have a few more questions regarding other settings in the design.

Q7. I used 40 rows and 5 blocks in this experiment (i.e., 8 choice tasks per respondent). When I tried a smaller number of rows, D-error tended to increase, and B-estimate tended to decrease (i.e., a status quo alternative being more dominant). Here's a summary of the results. Could you give me any suggestions on the number of rows and blocks?

• Settings .......... | D-error | A-error | B-estimate | S-estimate
  ------------------------------------------------------------------------------
  5 blocks, 40 rows | 4.36E-04 | 1.23E-03 | 2.955 | 1.552
  4 blocks, 32 rows | 5.21E-04 | 1.46E-03 | 1.338 | 2.008
  3 blocks, 24 rows | 6.99E-04 | 1.81E-03 | 1.090 | 2.654
  2 blocks, 16 rows | 9.64E-04 | 2.79E-03 | 0.764 | 3.997

Q8. For all attributes (b2 to b6) except for alternative-specific constant (b1 and b7), I used generic parameters to make the model simpler (i.e., a smaller number of parameters) given that a relatively small sample size would be expected. Do you any suggestions regarding the number of parameters given this small sample (e.g., 50-100)?

Q9. I also wonder if it'd be okay to use alternative-specific parameters for some of the attributes, when estimating the model, in case I will be able to get a larger number of responses (e.g., 300+)?

These are the questions that I currently have. Sorry if this is too many. And I'd greatly appreciate it if you could share with me any of your knowledge, experiences, and thoughts regarding these questions!

Thank you again,

Youngeun

[Michiel Bliemer]

Q1. An attribute with a single level is the same as a constant. If you already have alternative-specific constants included in your utility functions, you cannot add more constants since these parameters would not be identifiable in model estimation. The ASCs describe the labels, so 0% emissions becomes part of the ASC of battery electric vehicles and it is not possible to disentangle the utilities of "battery electic" and "0% emissions", they are representing by a single constant.

Q2. You are asking for an orthogonal design with a mix of numbers of attribute levels, namely a 7-level attribute, a 5-level attribute, a 2-level attribute, a 4-level attribute, and a 3-level attribute. Such an orthogonal design simply does not exist. Orthogonal designs where an attribute has 7 levels is very rare. To increase the likelihood of finding an orthogonal design, try to reduce the number of levels or use more similar numbers of levels, e.g. all 3 levels and a 6 level attribute or something. Note that orthogonal designs often do not exist, which is why you may want to use an efficient design (using zero priors), which will always exist without changing the numbers of levels. As you can see for example on this website, orthogonal arrays mostly exist for attributes with 2, 3, and 4 levels. For higher levels and with mixed levels, they are less likely to exist. http://neilsloane.com/oadir/

Q3. Relative changing in D-error are what is relevant. In your example, the second D-error is 3x as small as the first, which is rather large. The absolute value of the D-error is study specific, so it is the relative differences that matters. Note that you are NOT using random priors in your script, rather you are using random parameters and are assuming a logit model. To consider random (Bayesian) priors, you need to use round brackets, for example b1[(n,0.4800,0.1600)], please refer to the Ngene manual. Further, you would need ;bdraws instead of ;rdraws and you need to use ;eff = (mnl,d,mean) or ;eff = (mnl,d,median) to consider Bayesian priors. I would not recommend using random parameters (mixed logit) since optimising for mixed logit will not be computationally feasible in your case.

Q4. I would look at each choice task individually to assess whether they all make sense. Efficiency measures can only tell you about the statistical performance, but making sure that choice tasks are sensible requires some manual inspection.

Q5. A pilot survey typically consists of 10% of your expected final sample.

Q6. I would use an efficient design with noninformative priors, i.e. (near) zero priors, or an orthogonal design (if it exists). When using near zero priors, you can indicate the expected sign of the coefficient and use an * after each alternative name to let Ngene automatically remove dominant alternatives, see for example script below.

Code: Select all

Design
? orthogonal sequential
;alts = BEV*, HFCEV*, DSL*
;rows = 40
;block = 5
;eff = (mnl,d)
;model:
U(BEV) = b1 +
         b2[-0.0001]*pcostz[105,110,115,125,150,175,200] +
         b3[-0.0001]*ocostb[50,70] +
         b4[ 0.0001]*rangeb[100,200,300,500] +
         b5[-0.0001]*offsitez[10,20,60] +
         b6[-0.0001]*onsiteb[0,25,50,75,100] /

U(HFCEV)= b7 +
         b2*pcostz +
         b3*ocosth[90,115,130] +
         b4*rangeh[300,500,700] +
         b5*offsitez +
         b6*onsiteh[0,25,50,75,100] /

U(DSL) = b2*pcostd[100] +
         b3*ocostd[100] +
         b4*ranged[700] +
         b5*offsited[5]                         
$

Q7. The D-error will always increase when you increase the number of rows because it increases the number of observations. The minimum number of rows you theoretically need is (number of parameters) / (number of alternatives - 1) = 7 / 2 = 3.5 -> 4. To have sufficient variation in the data, you want to take a multiple of that, for example at least 3 times as much, e.g. 12 rows. Using a larger design will give you more variation in the data, so using 40 is fine, but you could use a smaller design if you want.

Q8.It is not possible to know in advance which parameters will be statistically significant and how many parameters you can estimate, this is very much case specific. It could be that you can estimate all parameters with 5-10 respondents, but sometimes you need hundreds or thousands. Your pilot study will give you some insights hopefully. Based on the parameter estimates from the pilot study, you may be able to use non-zero priors and get sample size estimates (if your estimates are sufficiently reliable).

Q9. Yes you can use alternative-specific coefficients in your utility functions. That will increase the number of parameters, but it you can design for it and later in model estimation you can still decide whether to make the coefficients alternative-specific or generic. Note that dominance checks with the * after each alternative will no longer work if you use alternative-specific coefficients since "dominance" is no longer defined in that case.

Michiel

[bye1830]

Dear Michiel,

All your answers are substantially helpful. I greatly appreciate your help! I'll ask you again if I have further questions.

Thank you again,

Youngeun