Raw utilities vs. Zero-Centered Diffs

Question

Hello,

I have a question about the raw utilities and Zero-Centered Diffs.

                   raw      Z-CDiffs
level 1    -0,333    -5,490
level 2    -0,212    -5,010
level 3    -0,013    -0,883
level 4    0,083    1,263
level 5    0,152    3,869
level 6    0,167    3,465
level 7    0,155    2,787

These utilities are from the same project in CBC using the HB estimation.
My question is why if I export the utilities in raw format and in Zero-Centered Diffs, there are differences in the structure of this attribute, i.e, the upper level in raw utilities is level 6, and the upper attribute in  Zero-Centered Diffs is level 5.

Many thanks
PB

Answer 1

Dear PB,

The Zero-Centered Diffs (ZCD) transformation happens at the individual respondent level.  It effectively "stretches" the utility scale, but it does so unequally across respondents:  respondents with noisier/smaller utilities get stretched more so that their utility ranges are comparable to those of respondents with less noisy/larger utilities, whose utilities get stretched less.  Because some respondents' utilities get stretched more than others, when we average across respondents, the relative rankings of raw and ZCD utilities can differ slightly.  

Note that if you run simulations (which use the raw utilities) results might differ a little from what you would expect from the report of mean ZCD utilities.  

For this reason among others it is often wise to keep the focus on simulations rather than on mean utilities (which suffer from the usual oddities that can happen with means, in addition to the one noted above).

Comments

Thanks so much!!