HB-Estimation results in equal standard deviations for two different linear utility coefficients

Question

Dear Sawtooth team,

I conducted a CBC analysis in which two attributes are of "numeric" nature. The attributes consist of 5 levels each and have equal distances between each level.

I estimated a hierarchical Bayes model (HB) from Sawtooth software to estimate a single coefficient for each "numeric" attribute - taking into account that I specified the value of the levels as single digits prior to running the model.

Due to the nature of the attributes both linear attributes were coded equally (namely from 1 – 5) in the X matrix.

The estimation results result in significantly different utility coefficients (as expected). However, interestingly, the reported standard errors for both coefficients are exactly the same.

Does this make sense? Is this the case since the levels were coded equally in the matrix? If I change the coding in the X matrix for one attribute, the standard error change (obviously).

Looking at the relative importance, the choice simulator as well as First Choice Hit Rates, I observe plausible results and significant different preferences for the two numeric attributes.
Estimating the model using a part-worth model (as a robustness check) leads to plausible results as well.

Still, I am wondering why I observe the same standard error for the two utility coefficients?

Thank you and best regards,
E.S.

Comments

Could you give me a bit more information?  If you're doing HB estimation for CBC data, you're probably either doing the analysis within our Lighthouse Studio platform or our standalone CBC/HB platform.

Where are you seeing Standard Error reported from either of these two software packages?  We report standard deviation, but not standard error (unless I'm forgetting something).

Or, are you looking at results for those coefficients as reported in one of our market simulator packages that accepts the utilities estimated from HB?

---

Dear Bryan,

thank you for your quick response and please excuse my imprecise description.

You are absolutely right – I am estimating a CBC/HB model within Light House Studio 9.9.2.

I am referring to equal standard deviations (not standard errors), which are reported in the „Summary“ tab of  the Analysis Manager of Light House Studio, after the CBC/HB model estimation.
I am getting different average utilities reported for both attributes but exactly the same standard deviations.

Obviously, calculating the standard deviations manually (using the individual utilities ) leads to the same results.

Settings: 20,000 iterations before using results; 20,000 draws uses for each respondent.

Edit: I have changed the settings to 100,000 iterations before using the results and 20,000 draws used for each respondent. That leads to the quasi same average utilities as before but results in standard deviations which are not equal anymore.

Answer 1

Good, we're talking standard deviation across respondent utilities from HB.  OK, sounds to me like it was just a fluke occurrence that the standard deviations were the same for those two parameters in your first run.  And, when you increased the number of iterations, you get a slightly different answer (which is expected).