# Linear attribute coding within the HB-estimation using zero centered values.

Dear Sawtooth Team,

I have a question regarding the linear attribute coding within the HB-estimation.

Imagine a CBC analysis that contains (besides other attributes) a price attribute having six levels with equal distances between the price levels.
The price levels are as follows: \$0; \$29.99; \$59,99; \$89.99; \$119.99; \$149.99.

I want to estimate a single utility coefficient for the price.

In order to meet the attribute coding guidelines, I made sure that the specified values metrically correspond to the quantities shown to respondents. Additionally the values have a magnitude of about single digits. Consequently, I coded them in the CBC/HB estimation settings as follows:
0; 0.2999; 0.5999; 0.8999; 1.1999; 1.4999.
However, I found that coding the attributes as zero centered values (i.e., -1.46, -0.88, -0.29, 0.29, 0.88, 1.46) seems to work better in terms of convergence.

I was wondering if that makes any sense. Especially since the helpfiles states that „CBC will automatically zero-center any values you specify when creating the independent variable matrix“.

When aiming for linear coding, is there generally a benefit in zero centering price values for the attribute coding?

Thank you and best regards,
E.S.
asked Nov 25, 2021

## 1 Answer

0 votes
Well, our software zero-centers the codes before conducting the utility estimation, so your level values would be converted to -0.75, -0.45, -0.15, 0.15, 0.45, and 0.75.

You stated that coding the attributes as -1.46 to +1.46 seemed to work better in terms of convergence.

In my experience, coding as -0.75 to +0.75 or coding as -1.46 to +1.46 should not matter much at all in terms of HB estimation convergence.

I'm wondering how you are assessing convergence...are you using a formal method such as Gelman-Rubin?
answered Nov 29, 2021 by Platinum (198,515 points)
Thank you Bryan for the answer.

Sorry for the -1.46 to +1.46. I copied the wrong line here. It is indeed as you wrote -0.75 to +0.75.

So if I got it right, there is no need to zero-center the levels myself, since the software zero-centers the codes prior to the utility estimation anyways.

Consequently there is no benefit in coding the attributes from -0.75 to +0.75 instead of o to 1.4999, as the estimates should be the same.

Thank you an best regards,
E.S.