# Scale of raw utilities

Dear Sawtooth community,

I am wondering how Lighthouse comes up with the scale of raw utilities:

1)    In particular, I am interested how you set/define the “zero-line” in effects-coding?
2)    Why isn’t the NONE-threshold (of an included dual-response none-option) the “zero-line”? Can I make the NONE value (which in my case is negative) the “zero-value” by simply adding its value to every level of each attribute?
3)    How could one “normalize” part-worths of different estimations so that they use the same scale, i.e., that one could directly compare results among different estimation strategies or sub-samples (e.g., performing a ttest)?

Thank you in advance for your support!

Best regards
asked Mar 13, 2017
retagged Mar 13, 2017

## 1 Answer

0 votes
Replies, in order:
1.  Because the analysis uses a special type of coding called "effects coding," the utilities are centered on zero - this means the utilities for an attribute's levels sum to zero.
2.  I suppose you could make none the reference level of your model, though I am not sure why you would want this.  Utilities are interval level measures, so like a temperature scale, the selection of the zero point is arbitrary.
3.  We do such a normalization with the zero-centered diffs transformation.
answered Mar 13, 2017 by Platinum (73,500 points)
Thank you for your immediate answer, Keith!

To 1) But the utilities can be centered to zero in many ways (i.e. by adding constants, see 2.), so how do you come up with that particular "zero"? And how would you interpret it?

To 2) If the NONE threshold would be the "zero", I could interpret a negative level as: "ceteris paribus this level decreases the probability of an alternative being chosen/bought". While I could not come up with that conclusion if the part-worth is between the NONE threshold and the zero-value(?). Or am I getting something wrong here?

So, is it correct to add the none-value to every attribute level in order that the NONE-threshold becomes zero?

To 3) As I understand SSI's "zero-centered differences" they also put weights on certain respondents, thus relative mean preferences could be different to relative means of raw utilities(?). How could I normalize and compare raw utilities without the obstacle of assigning different weights?

Thanks again!
1.  If you add a constant of 2 to all the utilities for an attribute they would NOT be zero-centered.

2.  You can NOT make any conclusions about the value of individual levels' utilities - because utilities are interval measures the zeros are not comparable from one attribute to the next - they do not share a universal zero.  I think you are interpreting zero way too strongly here.  I would encourage you to learn more about effects coding and about interval scaling.

3.  The zero centered diffs coding makes the utilities to have a common magnitude across respondents.  Necessarily this involves multiplying different respondent's utilities by different constants.  This will be appropriate for some applications (comparing utilities across groups) but not for others (e.g. running logit-based simulations).
Thank you again. Regarding 1 I meant by multiplying/dividing.

Regarding effects-coding: I read Lighthouse's tutorial, the "Getting started with Conjoint Analysis" book, and tried to find it standard statistics books. Can you recommend a source where I can learn more about effects coding?
1.  Yes, you could multiply the utilities by a constant and they will still be zero centered.  The raw utilities we use are scaled to predict choices using the logit choice rule, so unless you have a good reason to change that scaling (i.e. like wanting to make between-group comparisons) there is no good reason to do so.

We will have a chapter on different kinds of coding in our "Becoming and Expert in Conjoint Analysis" book but the "Getting Started" book is a good place to start.   A Google search I did just turned up 125 million hits and any of the ones on the first page looked valuable.