Underrepresented number of blocks in data analysis

[Andrew]

Hi,

in a CBC survey we applied different attributes with a different number of levels (6^1 x 4^1 x 3^2). The efficient design was created with 240 rows to cover many attribute-level-combinations, divided into 20 blocks. Each respondent was faced with 12 choice tasks each with 3 alternatives and no opt-out. Analyzing the data, we found out that some blocks have a much smaller number of respondents than other blocks. Thus, a few blocks are underrepresented within the data. One- and two-way frequencies across blocks, however, have a good level balance. So the question is: Does the over- or underrepresentation of blocks in the data have an effect on the overall efficiency of the design and, most important, on the analysis of choice data?

Regards,
Andrew

[Michiel Bliemer]

The fact that there is not perfect balance across blocks in the data may lead to some loss of efficiency, but it is not that important. You should use all your data for model estimation and not throw away any data in order to obtain equal representation of blocks.

Michiel

[Andrew]

Michiel,

thank you very much!
Could you recommend any paper on the subject using blocking technique with efficient designs? Mainly based on experience, I think choice experiments using attributes with very different numbers of levels require a large number of blocks in order to cover as many level-combinations as possible. And individual respondents are then not overwhelmed by too many choice scenarios. However, it is hard finding a paper that covers this issue.
And no, I wouldn't throw away any data without a very good reason.
Thanks again!

Kind regards,
Andrew

[Michiel Bliemer]

Blocking is typically associated with orthogonal arrays, blocking in efficient designs cannot be done perfectly and I am not aware of any literature that discusses this.

Note that many level-combinations are mainly needed when you are estimating a lot of interaction effects. For main effects, there is no need to include many different combinations.

Michiel