Table 1c.

Studies investigating the incorporation of choice behaviour on statistical efficiency

Author, Year	Outcome of interest	Method to create design	Design setting	Sample size	Choice sets	Altern-atives	Attri- butes	Attribute levels	Results
Crabbe, 2012 [33]	Local D-error	1)Individually adapted sequential Bayesian designs (IASB) with covariates incorporated 2)IASB designs, no covariates 3)single nearly orthogonal designs, no covariates	1)Choice behaviour is influenced by 2 covariates 2)Choice behaviour is NOT influenced by 2 (irrelevant) covariates	25, 250	16	3	3	3	Across all design settings and sample sizes: 1)Despite IASB designs incorporating two irrelevant covariates of participant behaviour, they still more statistically efficient than designs that do not incorporate any covariates. 2)IASB designs with two relevant covariates perform better (in terms of D-efficiency) in comparison to IASB designs with to irrelevant covariates, holding everything else constant.
Donkers, 2003 [37]	Average percentage change in D-error	Design incorporates the proportion of the population selecting y = 1, which varies from 2.5%, 5%, 10%, 15%, and 50% of the population. Results of D-error compared to random sampling from population.	.	Sample selection is dependent on proportion that selects Y = 1		2	2	1 binary, 1 continuous (Distribution of binary attribute when X = 1: 50% or 10% of the time)	1)As the proportion of the population selecting Y = 1 increases from 2.5% to 50%, D-efficiency improves. 2)As more individuals select 1, the magnitude of the reduction in D-error decreases (in comparison to when a random sample is used). The highest reduction in D-error (or improvement in D-efficiency) is when only 2.5% of the population selects y = 1. 3)Above results are consistent when binary attribute (x = 1) is distributed 10% or 50% of the time within the DCE.
Donkers, 2003 [37]	Average percentage change in D-error	Design incorporates the proportion of the population selecting y = 1, which varies from 2.5%, 5%, 10%, 15%, and 50% of the population. Results of D-error compared to random sampling from population.	.	Sample selection is dependent on: a)y only b)y and x c)x only		2	2	1 binary, 1 continuous; binary attribute is unevenly distributed with x = 1 only 10% of the time	Type of sample selection (y only, y and x, x only) 1)Designs with sample selection on both y and x yields higher statistical efficiency than designs with sample selection on y only or x only, where y is the outcome, and x is an attribute.