Design with design / scenario variables

[earpkin@leeds.ac.uk]

Dear Ngene experts,

Just wanted to query how to include “scenario” variables as in Section 8.5 of the manual ‘design within designs’. I didn’t find similar questions on the forum but please direct me if this has been suitably discussed before.
In our design we have three non-monetary attributes (att1, att2, att3) and one monetary (tax). On each choice card we provide pictures of a different species that the conservation plan could cover. This picture is the same across opt1, opt2, opt3 BUT varies across choice tasks. So, the first task pictures species1, the second species2 etc.

There are two research questions:
(1) how does the WTP for attributes 1,2,3 vary between medium and high levels,
(2) how does the species pictured on the choice card affect this WTP.
Minimum viable code:

Code: Select all

Design
;alts=opt1*, opt2*, opt3
;rows=18
;block=2
;eff=(mnl,d)
;model:
  U(opt1)=       
   
    b1.dummy[0.28|0.5] * att1[0,1,2]     +
    b2.dummy[0.14|0.25] * att2[0,1,2]     + 
    b3.dummy[0.15|0.25] * att3[0,1,2]  + 
    b4.dummy[-1|1] * species[0,1,2]         + 
    b5[-0.25] * tax[ 1, 2, 3, 4, 5, 6]/
   
    U(opt2)=       
      b1 * att1 +
      b2 * att2 + 
      b3 * att3 + 
      b4 * species[species] + 
      b5 * tax /
     
    U(opt3)=     sq[-1.50]
     
$

Questions:
1) Should we specify interactions between the attributes and the species in this syntax?
2) Is this the correct approach to interpreting the effect of ‘scenario’ variables?
Thanks for all your insight here and in the manual, best
Peter

[Michiel Bliemer]

With the specified model you only get a single WTP for each attribute 1,2,3 since species is only used as a main effect. For your second research question, you will need to make interactions between each attribute 1,2,3 and species. For example, for att1 you would need to add (note that the last level in Ngene is always the base level, so in your case level 2 is the base):

+ i1 * att1.dummy[0] * species.dummy[0]
+ i2 * att1.dummy[1] * species.dummy[0]
+ i3 * att1.dummy[0] * species.dummy[1]
+ i4 * att1.dummy[1] * species.dummy[1]

This means that you will need to estimate 12 more parameters for these interactions.

Regarding your first research question, it is unclear to me what you mean with medium and high levels. Are you referring to tax levels? For this research question, you may also need to make interactions, or otherwise estimate a nonlinear effect for tax, for example by also including the logarithm of tax as a main effect.

Michiel

[earpkin@leeds.ac.uk]

Dear Michiel,

Thank you for taking the time to evaluate this question!

Some clarifications:

“Regarding your first research question, it is unclear to me what you mean with medium and high levels. Are you referring to tax levels?”

. I apologise for the misunderstanding. In the actual experiment I will label the levels for att1, att2, att3 as “low” (0), “medium” (1), “high” (2).

Our research questions are thus
(1) to estimate WTP for the two non-reference levels of att1, att2, att3, and
(2) to evaluate how this WTP varies with different species. Following your kind suggestions, I have the following code:

Code: Select all

Design
;alts=opt1*, opt2*, opt3
;rows=18
;block=2
;eff=(mnl,d)
;model:
  U(opt1)=       
   
    b1.dummy[0.28|0.5] * att1[0,1,2]     +
    b2.dummy[0.14|0.25] * att2[0,1,2]     +
    b3.dummy[0.15|0.25] * att3[0,1,2]  +
    b4.dummy[-1|1] * species[0,1,2]         +
   
    b4.dummy[-1|1] * species[0,1,2]         +
   
    i1 * att1.dummy[0] * species.dummy[0] +
    i2 * att1.dummy[1] * species.dummy[0] +
    i3 * att1.dummy[0] * species.dummy[1] +
    i4 * att1.dummy[1] * species.dummy[1] +
    i5 * att2.dummy[0] * species.dummy[0] +
    i6 * att2.dummy[1] * species.dummy[0] +
    i7 * att2.dummy[0] * species.dummy[1] +
    i8 * att2.dummy[1] * species.dummy[1] +
    i9 * att3.dummy[0] * species.dummy[0] +
    i10 * att3.dummy[1] * species.dummy[0] +
    i11 * att3.dummy[0] * species.dummy[1] +
    i12 * att3.dummy[1] * species.dummy[1] +
   
    b5[-0.25] * tax[ 1, 2, 3, 4, 5, 6]/
   
   
    U(opt2) =
      b1 * att1 +
      b2 * att2 +
      b3 * att3 +
      b4 * species[species] +
      i1 * att1 * species +
      i2 * att1 * species +
      i3 * att1 * species +
      i4 * att1 * species +
      i5 * att2 * species +
      i6 * att2 * species +
      i7 * att2 * species +
      i8 * att2 * species +
      i9 * att3 * species +
      i10 * att3 * species +
      i11 * att3 * species +
      i12 * att3 * species +
      b5 * tax /
     
      U(opt3)=     sq[-1.50]
     
      $

Two questions:
A) Can I just confirm that in U(opt1) we don’t need to specify an interaction for species.dummy[2]?
B) We can then interpret the interactions as effects of that species on preferences for that attribute level?

Much appreciated

[Michiel Bliemer]

For any dummy coded attribute you can only includes L-1 dummy variables, whereby level L is the base. So all interpretations are relative to the base species in your case. That means that you can at most include 2 out of 3 species in the interaction, with the third being the base.

For example, suppose that you have:

b1.dummy[0.28|0.5] * att1[0,1,2] +
i1 * att1.dummy[0] * species.dummy[0] +
i2 * att1.dummy[1] * species.dummy[0] +
i3 * att1.dummy[0] * species.dummy[1] +
i4 * att1.dummy[1] * species.dummy[1] +

For species 2: b1(d0) and b1(d1) are the coefficients for att1 level 0 and 1, relative to zero utility for base level 2.
For species 0: b1(d0)+i1 and b1(d1)+i2 are the coefficients for att1 level 0 and 1, relative to zero utility for base level 2.
For species 1: b1(d0)+i3 and b1(d1)+i4 are the coefficients for att1 level 0 and 1, relative to zero utility for base level 2.

In other words, for each species, you have different coefficients for att1.

Michiel