A Monte Carlo Study of Design Procedures for the Semi-parametric Mixed Logit Model

Andreas Falke; Harald Hruschka

doi:10.1515/roms-2014-0002

Artikel

A Monte Carlo Study of Design Procedures for the Semi-parametric Mixed Logit Model

Andreas Falke und Harald Hruschka

Veröffentlicht/Copyright: 30. April 2016

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Abstract

We determine efficient designs for choice-based conjoint analysis for the semi-parametric mixed logit model which captures latent consumer heterogeneity in a very flexible way. Different methods constructing one or multiple designs are tested. Additionally we apply Halton draws and determine a minimum potential design for prior draws to reduce computation times caused by accounting for latent heterogeneity of consumers. As main efficiency criteria for the construction of designs we consider measures related to D-error and entropy. As additional benchmarks we generate designs both randomly and by an approach which starts from orthogonal designs developed for linear models. We compare these alternative design procedures by simulating choices for different constellations on the basis of the semi-parametric mixed logit model. Using these simulated choices we estimate parameters of the semi-parametric mixed logit model in the next step. ANOVA with root mean squared error between estimated and true coefficient values as dependent variable shows that performance of design procedures depends on dissimilarity and segment size. Following a mean-standard deviation approach we determine which procedure should be used under different constellations or lack of prior information. Overall, either constructing ten designs based on D_B-error or constructing one design based on entropy turn out to be preferable.

Keywords: semi-parametric semi-Bayesian mixed logit design; heterogeneity; estimation accuracy; multinomial logit design; D-optimality; entropy

Appendix 1: Estimation of the semi-parametric mixed logit model

We set initial segment shares to equal values, initial coefficients bc0 to a random value in the interval [β−2⋅σ,β+2⋅σ] with β being the true value of the consumer coefficient and σ=0.1, which is the higher value of factor 3. The initial covariance matrix is diagonal with all diagonal elements being 0.5. We initialize parameters this way, as we focus on the comparison of design procedures and do not intend to test estimation algorithms.

The proper estimation algorithm is taken from Train (2008):

For each person R=4 random values are drawn from the segment specific normal distribution N(bc0,Vc0). The r-th draw for person n in segment c is labeled as βˆncr0.
For each person in each segment and each draw a weight is calculated as
hncr0=gc0Knβˆncr0∑cgc∑rKnβˆncr0/R
with Kn(βˆncr0) as probability of y_n, conditional on βˆncr0
Kn(βˆncr0)=∏teβˆncr0xnyntt∑jeβˆncr0xnjt
Segment shares are updated as
gc1=∑n∑rhncr0∑′c∑n∑rhnc′r0
Coefficients and covariances are updated by
bc1=∑n∑rhncr0βˆncr0∑n∑rhncr0
and
Vc1=∑n∑rhncr0(βˆncr0−bc1)(βˆncr0−bc1)′∑n∑rhncr0,
respectively.
If the absolute difference between previous and updated parameter values is less than 10−6 or 10000 iterations have been made, the algorithm stops, otherwise it sets the old values of parameters to their updated values and goes back to step 1.

Appendix 2: Tables with designs

Table 4:

18 Choice sets, design 1.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	2	1	0	1	1	1	2	1	0	0	0
	II	0	0	2	1	0	1	0	0	0	1	1	1
2	I	0	1	0	2	2	2	1	1	1	1	1	2
	II	2	0	1	2	2	2	2	2	2	2	2	0
3	I	1	2	1	2	0	2	2	2	2	2	2	1
	II	0	1	0	0	1	1	0	0	0	0	0	2
4	I	2	2	2	1	2	0	0	0	1	1	2	1
	II	0	2	1	2	2	0	1	1	2	2	0	2
5	I	2	1	1	2	1	2	1	1	2	2	0	0
	II	0	0	2	1	1	2	2	2	0	0	1	1
6	I	1	2	1	2	0	1	2	2	0	0	1	2
	II	1	1	2	1	2	0	0	0	1	1	2	0
7	I	2	2	2	2	1	2	2	0	2	1	0	2
	II	1	0	1	1	0	1	0	1	0	2	1	0
8	I	1	1	2	2	1	1	0	1	0	2	1	1
	II	2	2	0	0	1	2	1	2	1	0	2	2
9	I	1	0	0	1	0	2	1	2	1	0	2	0
	II	2	2	1	0	2	2	2	0	2	1	0	1
10	I	0	2	2	2	2	2	1	0	2	0	1	1
	II	1	2	1	0	0	1	2	1	0	1	2	2
11	I	1	1	1	1	2	0	2	1	0	1	2	0
	II	2	1	0	0	0	1	0	2	1	2	0	1
12	I	1	2	2	0	2	0	0	2	1	2	0	2
	II	0	1	2	1	1	2	1	0	2	0	1	0
13	I	2	2	1	2	2	1	1	0	0	2	2	2
	II	0	2	2	0	1	2	2	1	1	0	0	0
14	I	0	1	2	2	2	2	2	1	1	0	0	1
	II	2	2	2	1	1	0	0	2	2	1	1	2
15	I	2	1	1	0	2	2	0	2	2	1	1	0
	II	2	0	0	1	2	1	1	0	0	2	2	1
16	I	2	2	2	1	1	0	2	0	1	2	1	0
	II	1	2	0	0	2	2	0	1	2	0	2	1
17	I	2	1	2	2	1	2	0	1	2	0	2	2
	II	0	1	1	1	0	1	1	2	0	1	0	0
18	I	1	1	2	2	0	1	1	2	0	1	0	1
	II	2	0	1	1	2	2	2	0	1	2	1	2

Table 5:

18 Choice sets, design 2.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	1	0	0	1	2	1	2	1	0	0	0
	II	2	0	1	2	2	0	2	0	2	1	1	1
2	I	1	0	0	1	2	1	0	1	1	1	1	2
	II	2	1	2	0	1	0	2	2	2	2	2	0
3	I	0	1	1	1	0	2	2	2	2	2	2	1
	II	1	0	2	0	2	1	0	0	0	0	0	2
4	I	1	1	1	1	1	2	0	0	1	1	2	1
	II	2	0	0	2	0	0	1	1	2	2	0	2
5	I	1	0	1	1	1	1	1	1	2	2	0	0
	II	2	1	2	0	2	0	2	2	0	0	1	1
6	I	2	2	1	2	2	1	2	2	0	0	1	2
	II	2	0	0	0	1	2	0	0	1	1	2	0
7	I	1	1	2	1	1	0	2	0	2	1	0	2
	II	2	0	1	0	2	1	0	1	0	2	1	0
8	I	0	1	1	1	1	1	0	1	0	2	1	1
	II	1	2	0	2	2	2	1	2	1	0	2	2
9	I	0	2	2	1	2	1	1	2	1	0	2	0
	II	1	1	1	2	1	0	2	0	2	1	0	1
10	I	2	0	1	1	1	2	1	0	2	0	1	1
	II	1	2	0	0	0	1	2	1	0	1	2	2
11	I	2	1	1	1	2	0	2	1	0	1	2	0
	II	0	1	2	2	1	2	0	2	1	2	0	1
12	I	1	2	1	2	1	0	0	2	1	2	0	2
	II	2	1	0	1	0	2	1	0	2	0	1	0
13	I	2	2	1	2	1	1	1	0	0	2	2	2
	II	0	0	2	0	0	2	2	1	1	0	0	0
14	I	0	1	2	2	2	2	2	1	1	0	0	1
	II	1	2	0	0	0	0	0	2	2	1	1	2
15	I	2	1	1	0	2	2	0	2	2	1	1	0
	II	0	2	2	1	0	0	1	0	0	2	2	1
16	I	0	1	0	2	1	0	2	0	1	2	1	0
	II	2	0	1	0	2	2	0	1	2	0	2	1
17	I	1	1	1	1	1	1	0	1	2	0	2	2
	II	0	2	0	0	2	0	1	2	0	1	0	0
18	I	1	1	2	2	0	1	1	2	0	1	0	1
	II	2	2	0	0	1	2	2	0	1	2	1	2

Table 6:

18 Choice sets, design 3.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	2	2	2	0	1	1	1	2	1	0	0	0
	II	0	0	1	2	2	0	2	0	2	1	1	1
2	I	2	0	0	2	1	2	0	1	1	1	1	2
	II	0	2	2	0	0	0	1	2	2	2	2	0
3	I	1	0	0	2	0	0	0	0	0	0	0	1
	II	0	0	1	0	2	0	0	2	0	0	0	0
4	I	1	2	1	1	1	1	0	0	1	1	2	1
	II	1	0	2	2	2	0	1	1	2	2	0	2
5	I	1	0	2	1	1	2	1	1	2	2	0	0
	II	1	2	1	2	2	0	2	2	0	0	1	1
6	I	2	2	1	1	1	2	2	2	0	0	1	2
	II	1	0	2	0	0	0	0	0	1	1	2	0
7	I	0	1	1	2	1	0	2	0	2	1	0	2
	II	1	2	0	0	2	2	0	1	0	2	1	0
8	I	1	1	1	0	1	0	0	1	0	2	1	1
	II	0	2	2	1	2	1	1	2	1	0	2	2
9	I	2	1	1	1	2	0	1	2	1	0	2	0
	II	1	0	0	2	1	1	2	0	2	1	0	1
10	I	1	2	2	1	1	1	1	0	2	0	1	1
	II	2	1	0	1	2	0	2	1	0	1	2	2
11	I	1	1	0	1	1	0	2	1	0	1	2	0
	II	2	1	1	2	0	2	0	2	1	2	0	1
12	I	0	2	1	1	2	0	0	2	1	2	0	2
	II	1	1	2	1	0	2	1	0	2	0	1	0
13	I	1	1	2	1	1	1	1	0	0	2	2	2
	II	0	0	1	1	2	1	2	1	1	0	0	0
14	I	0	1	1	1	2	1	2	1	1	0	0	1
	II	2	2	1	0	1	0	0	2	2	1	1	2
15	I	2	1	1	0	2	2	0	2	2	1	1	0
	II	0	2	2	1	0	0	1	0	0	2	2	1
16	I	0	1	0	2	1	0	2	0	1	2	1	0
	II	1	2	1	0	2	1	0	1	2	0	2	1
17	I	1	1	1	1	1	1	0	1	2	0	2	2
	II	2	2	2	2	2	2	1	2	0	1	0	0
18	I	1	1	2	2	0	1	1	2	0	1	0	1
	II	2	2	0	0	1	2	2	0	1	2	1	2

Table 7:

18 choice sets, design 4.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	1	1	1	2	0	0	1	2	1	0	0	0
	II	0	0	0	1	1	1	2	0	2	1	1	1
2	I	1	2	0	1	0	1	0	1	1	1	1	2
	II	0	0	2	0	1	0	1	2	2	2	2	0
3	I	2	0	2	1	2	0	0	0	0	0	0	1
	II	0	2	0	0	0	2	1	1	1	1	1	2
4	I	1	1	0	1	2	1	1	0	1	1	2	1
	II	0	2	2	2	0	2	1	1	2	2	0	2
5	I	0	2	1	2	1	1	1	1	2	2	0	0
	II	1	1	0	0	2	1	2	2	0	0	1	1
6	I	1	1	0	1	1	1	2	2	0	0	1	2
	II	2	0	1	1	2	0	0	0	1	1	2	0
7	I	2	1	0	1	1	2	2	0	2	1	0	2
	II	1	2	1	0	2	2	0	1	0	2	1	0
8	I	0	1	2	2	1	2	0	1	0	2	1	1
	II	1	2	0	1	2	1	1	2	1	0	2	2
9	I	1	1	2	1	1	2	1	2	1	0	2	0
	II	2	1	0	2	0	1	2	0	2	1	0	1
10	I	2	1	1	0	1	1	1	0	2	0	1	1
	II	1	0	0	1	2	2	2	1	0	1	2	2
11	I	0	1	2	1	0	2	2	1	0	1	2	0
	II	1	1	1	2	1	1	0	2	1	2	0	1
12	I	2	1	1	1	1	2	0	2	1	2	0	2
	II	1	0	2	2	0	1	1	0	2	0	1	0
13	I	1	0	1	1	1	2	1	0	0	2	2	2
	II	0	1	0	2	2	0	2	1	1	0	0	0
14	I	2	1	2	1	1	1	2	1	1	0	0	1
	II	1	2	1	2	0	2	0	2	2	1	1	2
15	I	1	1	1	2	1	1	0	2	2	1	1	0
	II	0	2	2	1	0	0	1	0	0	2	2	1
16	I	2	1	2	1	1	0	2	0	1	2	1	0
	II	0	2	1	0	2	2	0	1	2	0	2	1
17	I	0	0	1	0	1	1	0	1	2	0	2	2
	II	1	1	2	1	2	2	1	2	0	1	0	0
18	I	0	1	1	1	2	1	1	2	0	1	0	1
	II	1	2	0	0	1	2	2	0	1	2	1	2

Table 8:

18 choice sets, design 5.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	2	1	0	1	0	0	1	2	1	0	0	0
	II	0	1	1	0	2	2	2	0	2	1	1	1
2	I	2	1	0	1	0	2	0	1	1	1	1	2
	II	0	0	2	2	2	0	1	2	2	2	2	0
3	I	1	2	1	1	1	0	0	0	0	0	0	1
	II	0	1	0	2	0	2	1	1	1	1	1	2
4	I	1	2	0	1	1	0	1	0	1	1	2	1
	II	2	0	2	2	0	1	2	1	2	2	0	2
5	I	0	1	1	1	2	0	1	1	2	2	0	0
	II	2	0	2	2	2	2	2	2	0	0	1	1
6	I	0	1	2	2	2	1	2	2	0	0	1	2
	II	1	2	1	0	0	2	0	0	1	1	2	0
7	I	1	1	0	1	2	1	2	0	2	1	0	2
	II	2	2	2	2	0	0	0	1	0	2	1	0
8	I	0	0	1	1	1	1	0	1	0	2	1	1
	II	2	1	0	0	2	0	1	2	1	0	2	2
9	I	0	2	1	1	0	1	1	2	1	0	2	0
	II	2	0	0	2	1	0	2	0	2	1	0	1
10	I	1	1	1	0	1	0	1	0	2	0	1	1
	II	2	2	2	2	2	1	2	1	0	1	2	2
11	I	2	1	1	0	2	1	2	1	0	1	2	0
	II	0	2	0	1	1	0	0	2	1	2	0	1
12	I	1	1	1	2	0	1	0	2	1	2	0	2
	II	2	1	2	0	1	1	1	0	2	0	1	0
13	I	0	2	1	1	2	1	1	0	0	2	2	2
	II	1	1	2	2	0	0	2	1	1	0	0	0
14	I	1	0	1	1	1	0	2	1	1	0	0	1
	II	2	1	0	2	2	1	0	2	2	1	1	2
15	I	0	1	1	1	1	0	0	2	2	1	1	0
	II	1	2	2	0	1	1	1	0	0	2	2	1
16	I	1	1	1	1	1	2	2	0	1	2	1	0
	II	0	1	0	2	2	1	0	1	2	0	2	1
17	I	2	2	1	2	1	2	0	1	2	0	2	2
	II	1	1	2	1	2	0	1	2	0	1	0	0
18	I	2	0	1	1	1	1	1	2	0	1	0	1
	II	1	1	2	2	0	2	2	0	1	2	1	2

Table 9:

18 choice sets, design 6.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	2	2	2	0	0	0	1	2	1	0	0	0
	II	0	0	0	1	2	2	2	0	2	1	1	1
2	I	0	1	2	1	2	1	0	1	1	1	1	2
	II	0	1	0	2	1	0	1	2	2	2	2	0
3	I	2	1	0	2	0	2	0	0	0	0	0	1
	II	0	0	1	0	1	2	1	1	1	1	1	2
4	I	0	1	2	0	2	2	1	0	1	1	2	1
	II	1	0	1	1	0	0	2	1	2	2	0	2
5	I	1	2	0	1	1	0	1	1	2	2	0	0
	II	0	1	1	2	0	2	2	2	0	0	1	1
6	I	1	0	0	1	0	0	0	2	0	0	1	2
	II	0	2	2	0	1	1	0	0	1	1	2	0
7	I	1	2	2	1	1	1	2	0	2	1	0	2
	II	0	2	1	1	0	2	0	1	0	2	1	0
8	I	2	0	2	0	0	2	0	1	0	2	1	1
	II	1	2	0	1	1	0	1	2	1	0	2	2
9	I	0	1	1	0	2	0	1	2	1	0	2	0
	II	2	0	2	1	2	1	2	0	2	1	0	1
10	I	1	2	1	2	0	2	1	0	2	0	1	1
	II	0	0	2	1	1	1	2	1	0	1	2	2
11	I	1	0	1	0	1	1	2	1	0	1	2	0
	II	2	1	2	2	0	2	0	2	1	2	0	1
12	I	0	0	2	1	0	1	0	2	1	2	0	2
	II	2	1	0	0	2	2	1	0	2	0	1	0
13	I	2	2	0	2	1	2	1	0	0	2	2	2
	II	1	0	1	0	0	0	2	1	1	0	0	0
14	I	0	0	1	1	2	2	2	1	1	0	0	1
	II	2	2	2	2	0	1	0	2	2	1	1	2
15	I	2	2	1	1	1	2	0	2	2	1	1	0
	II	1	2	2	2	2	1	1	0	0	2	2	1
16	I	0	2	0	1	0	1	2	0	1	2	1	0
	II	2	0	1	1	1	0	0	1	2	0	2	1
17	I	1	1	0	1	1	1	0	1	2	0	2	2
	II	2	1	1	0	2	0	1	2	0	1	0	0
18	I	1	2	1	1	1	1	1	2	0	1	0	1
	II	2	2	2	2	2	2	2	0	1	2	1	2

Table 10:

18 choice sets, design 7.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	1	1	0	2	2	1	2	1	0	0	0
	II	2	0	0	2	1	1	2	0	2	1	1	1
2	I	2	1	1	2	1	0	0	1	1	1	1	2
	II	0	2	0	0	0	1	1	2	2	2	2	0
3	I	1	1	2	1	0	1	0	0	0	0	0	1
	II	0	1	2	0	2	0	1	1	1	1	1	2
4	I	0	1	1	0	1	1	1	0	1	1	2	1
	II	2	2	0	2	0	0	2	1	2	2	0	2
5	I	0	1	1	2	1	2	1	1	2	2	0	0
	II	2	2	0	0	1	1	2	2	0	0	1	1
6	I	2	2	2	1	2	2	0	2	0	0	1	2
	II	0	1	0	2	1	1	1	0	1	1	2	0
7	I	0	2	2	1	0	1	0	0	0	1	0	2
	II	1	0	0	2	1	2	0	0	0	2	1	0
8	I	1	2	1	2	2	1	0	1	0	2	1	1
	II	2	1	0	0	0	0	1	2	1	0	2	2
9	I	2	1	2	2	1	2	1	2	1	0	2	0
	II	2	2	0	0	0	1	2	0	2	1	0	1
10	I	0	1	0	1	2	1	1	0	2	0	1	1
	II	1	0	1	0	0	0	2	1	0	1	2	2
11	I	0	2	2	2	1	0	2	1	0	1	2	0
	II	1	1	0	1	2	1	0	2	1	2	0	1
12	I	2	2	1	1	2	0	0	2	1	2	0	2
	II	1	1	0	1	0	1	1	0	2	0	1	0
13	I	1	1	2	1	0	1	1	0	0	2	2	2
	II	2	0	2	0	1	1	2	1	1	0	0	0
14	I	2	2	0	1	1	1	2	1	1	0	0	1
	II	1	1	1	1	0	0	0	2	2	1	1	2
15	I	1	1	2	0	0	1	0	2	2	1	1	0
	II	0	0	0	1	1	0	1	0	0	2	2	1
16	I	2	1	2	2	2	0	2	0	1	2	1	0
	II	1	0	2	0	1	1	0	1	2	0	2	1
17	I	0	1	2	0	2	1	0	1	2	0	2	2
	II	1	2	1	1	0	2	1	2	0	1	0	0
18	I	0	1	1	0	1	1	1	2	0	1	0	1
	II	1	0	2	1	2	2	2	0	1	2	1	2

Table 11:

18 choice sets, design 8.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	0	1	2	1	1	1	2	1	0	0	0
	II	2	1	2	1	0	0	2	0	2	1	1	1
2	I	0	0	1	1	0	0	0	1	1	1	1	2
	II	2	1	2	0	1	2	1	2	2	2	2	0
3	I	0	0	1	1	1	0	0	0	0	0	0	1
	II	1	1	0	2	0	1	1	1	1	1	1	2
4	I	0	2	1	2	0	1	1	0	1	1	2	1
	II	2	0	2	1	1	1	2	1	2	2	0	2
5	I	0	0	1	1	0	1	1	1	2	2	0	0
	II	2	1	2	0	1	0	2	2	0	0	1	1
6	I	0	1	1	0	0	1	0	2	0	0	1	2
	II	1	2	0	1	2	0	1	0	1	1	2	0
7	I	2	2	1	1	0	1	0	0	0	1	0	2
	II	1	0	0	2	2	2	1	1	1	2	1	0
8	I	1	0	0	2	1	0	1	1	0	2	1	1
	II	0	1	2	0	0	1	1	2	1	0	2	2
9	I	1	1	1	1	1	1	1	2	1	0	2	0
	II	2	2	0	0	1	0	2	0	2	1	0	1
10	I	2	1	2	1	1	1	1	0	2	0	1	1
	II	1	2	2	2	0	2	2	1	0	1	2	2
11	I	2	1	1	1	1	2	2	1	0	1	2	0
	II	1	0	0	0	2	1	0	2	1	2	0	1
12	I	1	1	1	1	1	2	0	2	1	2	0	2
	II	2	0	2	2	0	1	1	0	2	0	1	0
13	I	0	2	1	1	2	1	1	0	0	2	2	2
	II	1	0	0	2	1	2	2	1	1	0	0	0
14	I	1	1	0	0	1	1	2	1	1	0	0	1
	II	2	0	2	1	2	2	0	2	2	1	1	2
15	I	0	1	1	2	2	2	0	2	2	1	1	0
	II	1	2	0	1	1	0	1	0	0	2	2	1
16	I	1	1	2	1	1	2	2	0	1	2	1	0
	II	2	2	1	0	0	1	0	1	2	0	2	1
17	I	2	1	1	0	1	1	0	1	2	0	2	2
	II	0	2	0	2	0	2	1	2	0	1	0	0
18	I	2	1	1	2	1	1	1	2	0	1	0	1
	II	1	2	2	0	2	2	2	0	1	2	1	2

Table 12:

18 choice sets, design 9.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	1	2	0	1	1	2	1	2	1	0	0	0
	II	2	1	1	0	2	0	2	0	2	1	1	1
2	I	1	0	0	1	2	2	0	1	1	1	1	2
	II	2	2	1	1	1	1	1	2	2	2	2	0
3	I	0	1	0	0	1	2	0	0	0	0	0	1
	II	2	0	1	1	2	1	1	1	1	1	1	2
4	I	1	1	0	1	2	0	1	0	1	1	2	1
	II	2	0	1	0	1	1	2	1	2	2	0	2
5	I	0	2	2	1	0	2	1	1	2	2	0	0
	II	2	1	0	2	2	0	2	2	0	0	1	1
6	I	0	0	0	2	2	2	0	2	0	0	1	2
	II	2	1	1	1	1	0	1	0	1	1	2	0
7	I	0	1	0	0	2	2	0	0	0	1	0	2
	II	0	0	1	1	1	0	1	1	1	2	1	0
8	I	0	2	1	1	1	2	1	1	0	2	1	1
	II	2	1	0	0	2	1	2	2	1	0	2	2
9	I	1	0	0	0	1	1	0	0	2	0	0	0
	II	1	2	1	2	2	2	0	0	0	1	0	0
10	I	0	0	1	0	1	1	1	0	2	0	1	1
	II	1	1	0	1	2	2	2	1	0	1	2	2
11	I	0	1	0	2	1	1	2	1	0	1	2	0
	II	1	2	1	0	2	0	0	2	1	2	0	1
12	I	1	1	2	1	2	1	0	2	1	2	0	2
	II	0	2	0	2	0	0	1	0	2	0	1	0
13	I	0	1	2	1	1	1	1	0	0	2	2	2
	II	2	0	0	2	0	2	2	1	1	0	0	0
14	I	1	2	0	2	2	1	2	1	1	0	0	1
	II	1	0	2	0	0	2	0	2	2	1	1	2
15	I	1	0	2	1	1	1	0	2	2	1	1	0
	II	0	1	0	0	0	0	1	0	0	2	2	1
16	I	1	2	1	1	1	1	2	0	1	2	1	0
	II	1	0	0	2	2	0	0	1	2	0	2	1
17	I	0	1	1	2	0	1	0	1	2	0	2	2
	II	1	2	2	1	1	2	1	2	0	1	0	0
18	I	0	0	2	1	1	0	1	2	0	1	0	1
	II	1	1	0	0	1	1	2	0	1	2	1	2

Table 13:

18 choice sets, design 10.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	1	0	2	0	1	1	2	1	0	0	0
	II	1	0	2	0	1	0	2	0	2	1	1	1
2	I	2	0	0	2	1	1	0	1	1	1	1	2
	II	1	2	2	0	0	0	1	2	2	2	2	0
3	I	0	2	2	0	1	1	0	0	0	0	0	1
	II	2	0	2	2	2	0	1	1	1	1	1	2
4	I	0	2	0	1	1	0	1	0	1	1	2	1
	II	1	0	2	2	0	2	2	1	2	2	0	2
5	I	1	1	1	1	2	1	1	1	2	2	0	0
	II	2	0	0	2	1	0	2	2	0	0	1	1
6	I	2	2	2	1	1	1	0	2	0	0	1	2
	II	1	2	2	0	0	0	1	0	1	1	2	0
7	I	0	1	2	0	1	1	0	0	0	1	0	2
	II	2	2	1	2	0	0	1	1	1	2	1	0
8	I	1	1	1	2	1	1	1	1	0	2	1	1
	II	0	0	2	0	2	0	2	2	1	0	2	2
9	I	1	0	2	0	0	1	0	0	2	0	0	0
	II	0	2	2	2	1	2	1	1	0	1	1	1
10	I	0	2	1	2	2	1	2	0	0	0	0	0
	II	1	1	2	1	0	2	0	1	0	0	0	0
11	I	1	1	0	1	0	1	2	1	0	1	2	0
	II	0	2	2	0	1	2	0	2	1	2	0	1
12	I	1	1	1	0	1	1	0	2	1	2	0	2
	II	0	2	0	1	0	2	1	0	2	0	1	0
13	I	1	2	1	1	0	1	1	0	0	2	2	2
	II	1	0	0	2	1	2	2	1	1	0	0	0
14	I	1	1	2	1	1	1	2	1	1	0	0	1
	II	1	0	1	0	0	2	0	2	2	1	1	2
15	I	1	0	1	2	1	2	0	2	2	1	1	0
	II	1	2	0	0	2	0	1	0	0	2	2	1
16	I	1	1	1	1	1	0	2	0	1	2	1	0
	II	0	0	2	2	2	1	0	1	2	0	2	1
17	I	2	0	1	1	2	1	0	1	2	0	2	2
	II	1	1	2	0	1	2	1	2	0	1	0	0
18	I	2	2	1	1	1	2	1	2	0	1	0	1
	II	1	2	0	2	2	1	2	0	1	2	1	2

Table 14:

27 choice sets, design 1.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	1	2	2	0	2	2	2	1	0	0	1
	II	2	0	1	1	2	0	0	0	2	1	1	2
2	I	2	1	2	1	1	1	0	1	1	2	2	1
	II	0	1	1	2	2	0	1	2	2	0	0	2
3	I	2	1	1	2	0	2	0	2	2	2	0	1
	II	0	0	0	1	2	1	1	0	0	0	1	2
4	I	0	2	2	0	1	2	0	0	0	0	2	2
	II	2	1	2	2	2	1	1	1	1	1	0	0
5	I	2	2	0	1	2	0	0	1	0	1	0	0
	II	1	0	2	2	1	2	1	2	1	2	1	1
6	I	2	1	1	0	1	2	0	2	1	0	1	0
	II	2	2	0	1	2	1	1	0	2	1	2	1
7	I	2	0	1	1	2	2	0	0	2	2	1	2
	II	2	1	2	2	1	1	1	1	0	0	2	0
8	I	2	2	0	2	1	2	0	1	2	1	2	0
	II	1	1	2	1	2	1	1	2	0	2	0	1
9	I	0	1	1	1	1	0	0	2	0	1	1	2
	II	1	2	2	0	2	2	1	0	1	2	2	0
10	I	2	2	2	1	2	2	1	0	0	2	0	0
	II	1	2	1	0	1	0	2	1	1	0	1	1
11	I	1	1	2	2	0	0	1	1	2	0	1	1
	II	1	2	1	2	1	1	2	2	0	1	2	2
12	I	2	1	1	0	2	2	1	2	2	0	2	2
	II	1	2	2	1	1	0	2	0	0	1	0	0
13	I	0	2	1	1	0	0	1	0	2	1	1	0
	II	1	1	2	2	1	2	2	1	0	2	2	1
14	I	1	1	1	1	2	2	1	1	1	1	0	2
	II	2	2	2	0	1	1	2	2	2	2	1	0
15	I	1	2	2	2	2	1	1	2	0	2	2	0
	II	2	1	1	1	0	2	2	0	1	0	0	1
16	I	2	2	1	1	1	1	1	0	1	1	1	1
	II	0	0	2	2	2	2	2	1	2	2	2	2
17	I	1	2	2	1	2	1	1	1	1	2	2	2
	II	2	0	1	0	1	0	2	2	2	0	0	0
18	I	1	2	0	2	0	0	1	2	0	0	0	1
	II	2	0	1	0	2	1	2	0	1	1	1	2
19	I	1	2	1	2	2	1	2	0	0	1	2	1
	II	1	1	2	1	1	2	0	1	1	2	0	2
20	I	1	1	1	0	2	0	2	1	2	0	0	0
	II	0	2	0	2	1	2	0	2	0	1	1	1
21	I	1	1	0	1	0	1	2	2	1	1	0	2
	II	0	0	1	2	2	0	0	0	2	2	1	0
22	I	1	1	2	2	1	2	2	0	1	0	2	0
	II	0	0	0	1	0	1	0	1	2	1	0	1
23	I	1	0	0	2	0	2	2	1	0	0	1	2
	II	0	1	2	0	1	1	0	2	1	1	2	0
24	I	1	1	1	1	1	0	2	2	2	1	2	1
	II	2	0	0	2	0	1	0	0	0	2	0	2
25	I	1	0	1	1	0	1	2	0	2	2	0	2
	II	0	2	2	0	2	2	0	1	0	0	1	0
26	I	1	1	0	1	1	1	2	1	0	2	1	1
	II	0	2	2	0	2	2	0	2	1	0	2	2
27	I	0	1	1	1	1	2	2	2	1	2	1	0
	II	1	0	2	0	2	1	0	0	2	0	2	1

Table 15:

27 choice sets, design 2.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	2	2	1	1	0	1	2	2	1	0	0	1
	II	2	0	0	2	2	0	0	0	2	1	1	2
2	I	2	1	1	0	0	1	0	0	1	2	2	1
	II	0	0	1	2	1	1	2	2	2	0	0	2
3	I	1	2	2	1	2	1	0	2	2	2	0	1
	II	1	1	0	0	1	0	1	0	0	0	1	2
4	I	0	1	2	0	1	1	0	0	0	0	2	2
	II	2	0	1	2	2	0	1	1	1	1	0	0
5	I	2	1	2	2	1	2	0	1	0	1	0	0
	II	1	0	1	0	0	1	1	2	1	2	1	1
6	I	1	2	2	2	1	2	0	2	1	0	1	0
	II	0	2	0	1	2	1	1	0	2	1	2	1
7	I	2	0	2	1	1	1	0	0	2	2	1	2
	II	1	2	0	2	2	0	1	1	0	0	2	0
8	I	0	1	2	1	0	2	0	1	2	1	2	0
	II	1	0	1	0	1	1	1	2	0	2	0	1
9	I	2	2	1	1	1	0	0	2	0	1	1	2
	II	2	0	2	2	2	2	1	0	1	2	2	0
10	I	1	1	1	0	2	2	1	0	0	2	0	0
	II	2	2	0	1	1	1	2	1	1	0	1	1
11	I	0	1	1	1	1	1	1	1	2	0	1	1
	II	1	2	0	0	2	2	2	2	0	1	2	2
12	I	2	1	0	1	1	1	1	2	2	0	2	2
	II	0	2	1	2	2	0	2	0	0	1	0	0
13	I	2	1	1	1	2	2	1	0	2	1	1	0
	II	1	0	2	2	1	1	2	1	0	2	2	1
14	I	0	0	1	1	1	2	1	1	1	1	0	2
	II	2	1	2	2	0	1	2	2	2	2	1	0
15	I	2	1	1	1	1	1	1	2	0	2	2	0
	II	0	0	0	0	0	1	2	0	1	0	0	1
16	I	0	1	1	2	2	1	1	0	1	1	1	1
	II	0	0	2	0	0	2	2	1	2	2	2	2
17	I	2	1	1	1	1	0	1	1	1	2	2	2
	II	0	0	0	2	0	1	2	2	2	0	0	0
18	I	0	1	2	1	2	2	1	2	0	0	0	1
	II	1	0	1	0	2	1	2	0	1	1	1	2
19	I	1	2	1	2	2	1	2	0	0	1	2	1
	II	2	0	2	0	0	2	0	1	1	2	0	2
20	I	1	1	1	0	2	0	2	1	2	0	0	0
	II	2	2	2	1	0	1	0	2	0	1	1	1
21	I	1	1	0	1	2	1	2	2	1	1	0	2
	II	2	2	2	2	1	2	0	0	2	2	1	0
22	I	1	1	1	1	0	1	2	0	1	0	2	0
	II	2	2	0	0	1	0	0	1	2	1	0	1
23	I	1	0	2	1	2	1	2	1	0	0	1	2
	II	2	2	1	0	1	0	0	2	1	1	2	0
24	I	1	1	1	1	1	2	2	2	2	1	2	1
	II	2	2	2	2	2	1	0	0	0	2	0	2
25	I	2	2	1	1	0	2	2	0	2	2	0	2
	II	0	1	2	2	2	0	0	1	0	0	1	0
26	I	1	1	0	1	1	1	2	1	0	2	1	1
	II	2	2	1	2	2	2	0	2	1	0	2	2
27	I	0	1	1	2	1	1	2	2	1	2	1	0
	II	2	2	2	1	2	0	0	0	2	0	2	1

Table 16:

27 choice sets, design 3.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	1	1	0	0	2	2	2	2	1	0	0	1
	II	0	0	1	1	0	0	0	0	2	1	1	2
2	I	1	0	2	2	2	1	0	0	1	2	2	1
	II	0	1	0	1	1	2	1	1	2	0	0	2
3	I	1	0	0	2	1	2	0	0	2	2	0	1
	II	0	2	2	1	2	2	2	0	0	0	1	2
4	I	1	1	2	0	1	0	0	0	0	0	2	2
	II	2	0	0	2	2	1	1	1	1	1	0	0
5	I	0	2	1	1	0	1	0	1	0	1	0	0
	II	1	0	0	1	1	2	1	2	1	2	1	1
6	I	0	0	1	1	0	1	0	2	1	0	1	0
	II	2	0	2	2	1	0	1	0	2	1	2	1
7	I	0	2	1	1	1	1	0	0	2	2	1	2
	II	1	1	0	1	2	2	1	1	0	0	2	0
8	I	2	1	1	0	2	1	0	1	2	1	2	0
	II	0	2	2	1	1	2	1	2	0	2	0	1
9	I	0	1	2	1	0	0	0	2	0	1	1	2
	II	1	1	1	2	1	2	1	0	1	2	2	0
10	I	0	1	1	2	1	1	1	0	0	2	0	0
	II	1	2	2	1	0	0	2	1	1	0	1	1
11	I	2	2	0	1	1	1	1	1	2	0	1	1
	II	1	0	1	2	2	2	2	2	0	1	2	2
12	I	1	1	2	1	1	2	1	2	2	0	2	2
	II	2	2	1	2	2	0	2	0	0	1	0	0
13	I	2	0	1	1	1	1	1	0	2	1	1	0
	II	1	1	2	2	0	0	2	1	0	2	2	1
14	I	2	2	1	1	1	1	1	1	1	1	0	2
	II	1	1	2	2	2	0	2	2	2	2	1	0
15	I	1	1	0	0	1	2	1	2	0	2	2	0
	II	0	2	1	1	1	0	2	0	1	0	0	1
16	I	0	1	1	1	1	0	1	0	1	1	1	1
	II	2	1	2	0	0	1	2	1	2	2	2	2
17	I	1	1	1	2	1	0	1	1	1	2	2	2
	II	0	2	2	0	2	2	2	2	2	0	0	0
18	I	0	1	1	1	1	1	1	2	0	0	0	1
	II	1	2	0	2	0	0	2	0	1	1	1	2
19	I	2	1	1	1	1	1	2	0	0	1	2	1
	II	0	0	2	0	0	2	0	1	1	2	0	2
20	I	0	2	1	0	1	0	2	1	2	0	0	0
	II	2	0	2	2	0	2	0	2	0	1	1	1
21	I	0	0	2	1	1	1	2	2	1	1	0	2
	II	1	1	1	2	0	2	0	0	2	2	1	0
22	I	2	1	1	0	0	1	2	0	1	0	2	0
	II	0	2	2	1	2	2	0	1	2	1	0	1
23	I	1	2	1	1	1	1	2	1	0	0	1	2
	II	2	1	2	2	0	2	0	2	1	1	2	0
24	I	0	1	1	1	1	2	2	2	2	1	2	1
	II	1	2	2	2	2	1	0	0	0	2	0	2
25	I	1	1	1	1	2	1	2	0	2	2	0	2
	II	1	0	2	2	1	0	0	1	0	0	1	0
26	I	1	0	2	1	2	0	2	1	0	2	1	1
	II	0	1	1	2	0	1	0	2	1	0	2	2
27	I	0	1	1	2	1	1	2	2	1	2	1	0
	II	1	2	2	0	2	2	0	0	2	0	2	1

Table 17:

27 choice sets, design 4.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	2	0	0	1	1	2	2	1	0	0	1
	II	1	0	2	2	0	0	0	0	2	1	1	2
2	I	0	2	1	1	1	2	0	0	1	2	2	1
	II	1	2	0	0	0	0	1	1	2	0	0	2
3	I	2	2	0	1	1	1	0	0	2	2	0	1
	II	0	2	2	0	2	0	1	1	0	0	1	2
4	I	0	0	1	1	2	2	1	0	0	0	2	2
	II	2	1	1	0	0	1	0	1	1	1	0	0
5	I	0	1	2	0	2	0	0	1	0	1	0	0
	II	2	0	0	1	0	1	1	2	1	2	1	1
6	I	0	0	2	0	2	1	0	2	1	0	1	0
	II	2	2	0	1	1	2	1	0	2	1	2	1
7	I	0	1	2	2	2	1	0	0	2	2	1	2
	II	2	0	1	0	0	2	1	1	0	0	2	0
8	I	2	1	0	0	1	1	0	1	2	1	2	0
	II	1	2	1	2	0	2	1	2	0	2	0	1
9	I	1	1	1	2	2	0	0	2	0	1	1	2
	II	0	2	0	0	1	2	1	0	1	2	2	0
10	I	0	0	2	1	1	1	1	0	0	2	0	0
	II	2	1	0	0	2	2	2	1	1	0	1	1
11	I	2	0	2	1	1	1	1	1	2	0	1	1
	II	0	1	1	2	2	2	2	2	0	1	2	2
12	I	0	1	1	0	1	1	1	2	2	0	2	2
	II	1	2	0	1	2	0	2	0	0	1	0	0
13	I	1	2	1	1	2	0	1	0	2	1	1	0
	II	2	2	1	2	0	1	2	1	0	2	2	1
14	I	1	1	2	0	1	1	1	1	1	1	0	2
	II	0	0	0	1	2	2	2	2	2	2	1	0
15	I	0	1	2	2	1	0	1	2	0	2	2	0
	II	1	2	1	1	2	2	2	0	1	0	0	1
16	I	2	0	1	1	1	2	1	0	1	1	1	1
	II	1	1	1	2	2	1	2	1	2	2	2	2
17	I	0	1	1	1	1	2	1	1	1	2	2	2
	II	1	2	2	0	2	1	2	2	2	0	0	0
18	I	1	0	1	1	1	1	1	2	0	0	0	1
	II	0	1	2	2	2	2	2	0	1	1	1	2
19	I	1	1	1	1	0	1	2	0	0	1	2	1
	II	2	2	2	2	1	2	0	1	1	2	0	2
20	I	2	1	1	2	1	2	2	1	2	0	0	0
	II	1	0	2	1	2	1	0	2	0	1	1	1
21	I	2	2	1	1	1	1	2	2	1	1	0	2
	II	1	1	0	2	1	2	0	0	2	2	1	0
22	I	1	1	1	2	2	1	2	0	1	0	2	0
	II	0	2	2	1	1	2	0	1	2	1	0	1
23	I	0	1	1	2	2	1	2	1	0	0	1	2
	II	1	0	2	0	0	2	0	2	1	1	2	0
24	I	1	1	2	1	2	1	2	2	2	1	2	1
	II	0	2	0	2	0	0	0	0	0	2	0	2
25	I	0	1	0	1	1	1	2	0	2	2	0	2
	II	1	2	1	2	0	2	0	1	0	0	1	0
26	I	0	2	1	1	1	2	2	1	0	2	1	1
	II	1	1	0	2	0	1	0	2	1	0	2	2
27	I	2	0	1	1	2	0	2	2	1	2	1	0
	II	0	1	2	0	0	1	0	0	2	0	2	1

Table 18:

27 choice sets, design 5.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	2	2	1	0	0	1	2	2	1	0	0	1
	II	0	0	2	1	1	2	0	0	2	1	1	2
2	I	0	0	1	2	2	1	0	0	1	2	2	1
	II	1	1	2	0	0	2	1	1	2	0	0	2
3	I	0	0	2	2	0	1	0	0	2	2	0	1
	II	1	1	0	0	1	2	1	1	0	0	1	2
4	I	1	0	0	0	2	2	1	0	0	0	2	2
	II	2	1	1	1	0	0	0	1	1	1	0	0
5	I	0	2	0	0	0	0	0	1	0	1	0	0
	II	0	0	0	0	0	1	1	2	1	2	1	1
6	I	0	2	1	0	1	0	0	2	1	0	1	0
	II	1	0	2	1	2	1	1	0	2	1	2	1
7	I	0	0	2	2	1	2	0	0	2	2	1	2
	II	1	1	0	0	2	0	1	1	0	0	2	0
8	I	0	1	2	1	2	0	0	1	2	1	2	0
	II	1	2	0	2	0	1	1	2	0	2	0	1
9	I	0	2	0	1	1	2	0	2	0	1	1	2
	II	1	0	1	2	2	0	1	0	1	2	2	0
10	I	1	0	0	2	0	0	1	0	0	2	0	0
	II	2	1	1	0	1	1	2	1	1	0	1	1
11	I	1	1	2	0	1	1	1	1	2	0	1	1
	II	2	2	0	1	2	2	2	2	0	1	2	2
12	I	1	2	2	0	2	2	1	2	2	0	2	2
	II	2	0	0	1	0	0	2	0	0	1	0	0
13	I	1	0	2	1	1	0	1	0	2	1	1	0
	II	2	1	0	2	2	1	2	1	0	2	2	1
14	I	1	1	1	1	0	2	1	1	1	1	0	2
	II	2	2	2	2	1	0	2	2	2	2	1	0
15	I	2	1	1	1	1	0	1	2	0	2	2	0
	II	1	0	0	0	2	2	2	0	1	0	0	1
16	I	0	0	2	1	2	1	1	0	1	1	1	1
	II	2	2	0	2	0	0	2	1	2	2	2	2
17	I	2	2	1	0	2	2	1	1	1	2	2	2
	II	0	1	2	1	0	0	2	2	2	0	0	0
18	I	2	0	1	1	2	1	1	2	0	0	0	1
	II	0	2	2	2	0	2	2	0	1	1	1	2
19	I	0	2	1	1	2	1	2	0	0	1	2	1
	II	2	0	2	1	1	2	0	1	1	2	0	2
20	I	2	2	1	1	0	1	2	1	2	0	0	0
	II	0	0	2	0	1	0	0	2	0	1	1	1
21	I	1	1	1	0	1	0	2	2	1	1	0	2
	II	0	0	2	1	2	1	0	0	2	2	1	0
22	I	0	1	2	2	1	1	2	0	1	0	2	0
	II	0	2	0	1	0	2	0	1	2	1	0	1
23	I	2	1	1	1	1	1	2	1	0	0	1	2
	II	1	1	2	0	0	2	0	2	1	1	2	0
24	I	2	2	2	1	1	0	2	2	2	1	2	1
	II	0	0	1	1	2	1	0	0	0	2	0	2
25	I	0	1	2	1	1	2	2	0	2	2	0	2
	II	2	2	1	2	2	0	0	1	0	0	1	0
26	I	1	2	1	1	1	2	2	1	0	2	1	1
	II	2	0	2	2	2	0	0	2	1	0	2	2
27	I	1	0	1	1	1	2	2	2	1	2	1	0
	II	2	2	2	1	2	1	0	0	2	0	2	1

Table 19:

27 choice sets, design 6.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	2	1	0	1	1	1	2	2	1	0	0	1
	II	1	2	2	0	0	0	0	0	2	1	1	2
2	I	2	1	1	1	0	0	0	0	1	2	2	1
	II	0	2	0	0	2	1	1	1	2	0	0	2
3	I	2	1	1	2	1	1	0	0	2	2	0	1
	II	0	1	0	1	0	0	1	1	0	0	1	2
4	I	1	1	0	1	1	2	1	0	0	0	2	2
	II	0	0	2	0	1	0	2	1	1	1	0	0
5	I	1	0	1	2	0	2	0	2	0	0	0	0
	II	0	2	0	0	2	0	1	0	1	1	1	1
6	I	0	1	1	2	2	1	2	2	1	0	1	0
	II	2	2	2	2	0	2	0	0	2	1	2	1
7	I	0	1	1	1	1	2	0	0	2	2	1	2
	II	2	0	0	0	0	1	1	1	0	0	2	0
8	I	1	1	0	1	1	0	0	1	2	1	2	0
	II	0	0	2	0	2	1	1	2	0	2	0	1
9	I	1	1	2	2	0	1	0	2	0	1	1	2
	II	1	2	0	0	1	0	1	0	1	2	2	0
10	I	1	1	1	0	1	1	1	0	0	2	0	0
	II	0	0	0	1	2	2	2	1	1	0	1	1
11	I	1	2	2	2	2	2	1	1	2	0	1	1
	II	0	1	0	1	1	0	2	2	0	1	2	2
12	I	2	1	1	2	2	2	1	2	2	0	2	2
	II	1	2	2	0	1	0	2	0	0	1	0	0
13	I	0	1	2	0	1	2	1	0	2	1	1	0
	II	0	0	0	2	2	1	2	1	0	2	2	1
14	I	2	2	1	0	2	1	1	1	1	1	0	2
	II	1	0	2	2	1	0	2	2	2	2	1	0
15	I	2	1	2	1	1	0	1	2	0	2	2	0
	II	0	1	0	2	1	2	2	0	1	0	0	1
16	I	2	2	1	0	1	1	1	0	1	1	1	1
	II	1	1	0	1	0	1	2	1	2	2	2	2
17	I	1	1	1	2	1	1	1	1	1	2	2	2
	II	0	0	2	2	0	0	2	2	2	0	0	0
18	I	2	0	1	1	1	0	1	2	0	0	0	1
	II	0	2	2	2	0	1	2	0	1	1	1	2
19	I	0	1	1	1	1	0	2	0	0	1	2	1
	II	1	0	2	2	0	1	0	1	1	2	0	2
20	I	1	1	1	1	0	1	2	1	2	0	0	0
	II	0	0	2	2	1	2	0	2	0	1	1	1
21	I	2	1	1	2	1	2	2	2	1	1	0	2
	II	0	1	2	1	2	1	0	0	2	2	1	0
22	I	2	1	1	1	1	0	2	0	1	0	2	0
	II	1	1	0	0	2	1	0	1	2	1	0	1
23	I	1	1	1	2	1	1	2	1	0	0	1	2
	II	0	1	2	1	2	2	0	2	1	1	2	0
24	I	1	1	1	1	1	0	2	2	2	1	2	1
	II	0	0	0	2	2	2	0	0	0	2	0	2
25	I	2	1	1	1	1	1	2	0	2	2	0	2
	II	1	1	0	2	2	0	0	1	0	0	1	0
26	I	1	1	1	2	1	1	2	1	0	2	1	1
	II	2	0	2	0	2	0	0	2	1	0	2	2
27	I	1	0	0	1	1	1	2	2	1	2	1	0
	II	2	2	1	2	2	0	0	0	2	0	2	1

Table 20:

27 choice sets, design 7.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	2	2	1	0	1	2	2	1	0	0	1
	II	2	0	1	2	1	2	0	0	2	1	1	2
2	I	0	1	0	0	2	2	0	0	1	2	2	1
	II	2	2	1	1	1	1	1	1	2	0	0	2
3	I	0	0	0	1	2	0	0	0	2	2	0	1
	II	2	1	1	0	0	1	1	1	0	0	1	2
4	I	0	2	2	2	1	1	1	0	0	0	2	2
	II	1	0	1	0	2	0	2	1	1	1	0	0
5	I	0	2	1	1	0	1	0	2	0	0	0	0
	II	1	1	2	0	2	0	1	0	1	1	1	1
6	I	0	2	0	1	1	0	2	2	1	0	1	0
	II	2	0	1	0	0	1	0	0	2	1	2	1
7	I	1	0	2	2	2	2	0	0	0	0	1	0
	II	0	1	1	0	2	0	2	0	0	0	0	0
8	I	0	1	2	1	1	2	0	1	2	1	2	0
	II	2	2	1	2	2	1	1	2	0	2	0	1
9	I	0	1	1	1	2	1	0	2	0	1	1	2
	II	1	2	0	0	1	2	1	0	1	2	2	0
10	I	0	0	2	0	2	2	1	0	0	2	0	0
	II	1	1	0	2	0	0	2	1	1	0	1	1
11	I	0	1	1	1	1	2	1	1	2	0	1	1
	II	1	0	0	0	2	1	2	2	0	1	2	2
12	I	1	0	1	1	1	1	1	2	2	0	2	2
	II	2	1	2	0	0	0	2	0	0	1	0	0
13	I	2	1	2	2	0	2	1	0	2	1	1	0
	II	1	2	0	1	1	1	2	1	0	2	2	1
14	I	2	1	0	2	1	1	1	1	1	1	0	2
	II	1	0	1	1	0	2	2	2	2	2	1	0
15	I	1	2	1	1	2	0	1	2	0	2	2	0
	II	2	0	0	1	0	2	2	0	1	0	0	1
16	I	1	1	2	2	1	1	1	0	1	1	1	1
	II	2	0	0	1	2	2	2	1	2	2	2	2
17	I	0	0	1	1	1	1	1	1	1	2	2	2
	II	2	1	2	0	2	2	2	2	2	0	0	0
18	I	2	2	1	1	1	2	1	2	0	0	0	1
	II	0	1	2	2	2	1	2	0	1	1	1	2
19	I	2	1	1	1	1	1	2	0	0	1	2	1
	II	1	2	2	2	2	2	0	1	1	2	0	2
20	I	0	2	1	1	2	2	2	1	2	0	0	0
	II	1	0	2	2	1	0	0	2	0	1	1	1
21	I	1	1	0	1	1	1	2	2	1	1	0	2
	II	2	2	1	0	2	0	0	0	2	2	1	0
22	I	2	1	1	1	2	2	2	0	1	0	2	0
	II	0	2	2	2	0	1	0	1	2	1	0	1
23	I	0	1	1	1	0	0	2	1	0	0	1	2
	II	1	2	2	0	1	1	0	2	1	1	2	0
24	I	0	1	0	0	2	2	2	2	2	1	2	1
	II	2	2	1	1	0	1	0	0	0	2	0	2
25	I	1	1	2	1	1	1	2	0	2	2	0	2
	II	0	2	0	2	1	2	0	1	0	0	1	0
26	I	0	1	1	2	1	2	2	1	0	2	1	1
	II	1	2	2	1	2	0	0	2	1	0	2	2
27	I	0	2	2	1	1	1	2	2	1	2	1	0
	II	1	1	1	2	2	2	0	0	2	0	2	1

Table 21:

27 choice sets, design 8.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	1	1	0	2	1	2	2	1	0	0	1
	II	2	0	0	1	1	2	0	0	2	1	1	2
2	I	2	2	0	2	1	1	0	0	1	2	2	1
	II	1	0	2	1	0	0	1	1	2	0	0	2
3	I	0	0	2	2	1	0	0	0	2	2	0	1
	II	2	2	1	0	0	2	1	1	0	0	1	2
4	I	0	1	1	1	0	0	1	0	0	0	2	2
	II	2	0	0	0	1	1	2	1	1	1	0	0
5	I	1	1	0	2	2	1	0	2	0	0	0	0
	II	0	0	1	0	1	2	1	0	1	1	1	1
6	I	2	2	2	0	1	0	2	2	1	0	1	0
	II	1	0	1	1	2	2	0	0	2	1	2	1
7	I	1	2	1	1	1	1	0	0	0	0	1	0
	II	2	2	0	0	0	0	1	1	1	1	2	1
8	I	0	1	0	0	0	1	0	0	0	1	0	0
	II	2	0	2	2	1	0	0	0	0	0	0	1
9	I	0	1	2	1	1	1	0	2	0	1	1	2
	II	2	2	0	2	0	2	1	0	1	2	2	0
10	I	0	2	1	0	1	1	1	0	0	2	0	0
	II	2	1	2	2	0	0	2	1	1	0	1	1
11	I	0	0	2	2	1	1	1	1	2	0	1	1
	II	2	1	0	0	2	0	2	2	0	1	2	2
12	I	1	2	1	2	1	1	1	2	2	0	2	2
	II	0	1	2	0	2	2	2	0	0	1	0	0
13	I	0	1	1	1	2	1	1	0	2	1	1	0
	II	1	2	2	0	1	0	2	1	0	2	2	1
14	I	0	1	0	1	1	1	1	1	1	1	0	2
	II	1	2	2	0	2	2	2	2	2	2	1	0
15	I	1	1	0	2	1	2	1	2	0	2	2	0
	II	1	0	1	0	0	1	2	0	1	0	0	1
16	I	0	1	1	1	0	1	1	0	1	1	1	1
	II	1	2	0	0	1	2	2	1	2	2	2	2
17	I	1	2	1	2	0	1	1	1	1	2	2	2
	II	2	1	2	1	1	2	2	2	2	0	0	0
18	I	2	1	1	1	1	1	1	2	0	0	0	1
	II	1	0	2	2	2	0	2	0	1	1	1	2
19	I	0	0	1	1	2	1	2	0	0	1	2	1
	II	1	1	2	2	0	2	0	1	1	2	0	2
20	I	2	1	1	1	1	1	2	1	2	0	0	0
	II	1	0	2	2	0	0	0	2	0	1	1	1
21	I	1	1	2	1	1	1	2	2	1	1	0	2
	II	0	2	1	2	2	2	0	0	2	2	1	0
22	I	2	0	1	1	1	1	2	0	1	0	2	0
	II	0	1	2	2	0	0	0	1	2	1	0	1
23	I	0	1	1	2	0	2	2	1	0	0	1	2
	II	2	2	2	1	2	1	0	2	1	1	2	0
24	I	1	1	0	2	1	1	2	2	2	1	2	1
	II	0	2	2	1	0	0	0	0	0	2	0	2
25	I	0	1	1	0	1	1	2	0	2	2	0	2
	II	1	2	0	1	2	2	0	1	0	0	1	0
26	I	1	1	1	1	1	1	2	1	0	2	1	1
	II	0	2	2	0	2	0	0	2	1	0	2	2
27	I	1	1	1	1	0	1	2	2	1	2	1	0
	II	0	0	0	2	1	2	0	0	2	0	2	1

Table 22:

27 choice sets, design 9.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	0	2	2	1	2	2	2	1	0	0	1
	II	2	1	0	1	0	0	0	0	2	1	1	2
2	I	1	1	0	1	2	1	0	0	1	2	2	1
	II	0	0	2	0	0	1	1	1	2	0	0	2
3	I	2	1	1	1	0	0	0	0	2	2	0	1
	II	1	0	0	0	1	2	1	1	0	0	1	2
4	I	1	0	0	2	0	2	1	0	0	0	2	2
	II	0	1	1	0	2	2	2	1	1	1	0	0
5	I	1	0	2	1	1	0	0	2	0	0	0	0
	II	2	1	0	0	0	1	1	0	1	1	1	1
6	I	1	1	1	0	1	0	2	2	1	0	1	0
	II	0	0	0	2	2	2	0	0	2	1	2	1
7	I	0	1	0	1	2	2	0	0	0	0	1	0
	II	1	0	1	2	0	0	1	1	1	1	2	1
8	I	0	1	2	2	2	1	0	0	0	1	0	0
	II	2	2	1	1	1	2	1	1	1	2	1	1
9	I	0	1	2	1	1	2	0	2	0	1	1	2
	II	2	2	1	2	2	0	1	0	1	2	2	0
10	I	0	1	2	2	1	1	1	0	0	2	0	0
	II	2	0	0	1	2	2	2	1	1	0	1	1
11	I	1	2	1	1	0	1	1	1	2	0	1	1
	II	2	1	0	0	1	2	2	2	0	1	2	2
12	I	1	1	0	1	1	1	1	2	2	0	2	2
	II	1	0	1	0	2	2	2	0	0	1	0	0
13	I	0	1	2	1	1	1	1	0	2	1	1	0
	II	2	2	0	2	0	2	2	1	0	2	2	1
14	I	1	0	0	1	1	1	1	1	1	1	0	2
	II	0	1	2	2	2	2	2	2	2	2	1	0
15	I	2	0	2	1	1	1	1	2	0	2	2	0
	II	1	1	0	0	2	0	2	0	1	0	0	1
16	I	2	1	1	0	2	1	1	0	1	1	1	1
	II	1	2	2	1	1	2	2	1	2	2	2	2
17	I	0	1	1	1	2	1	1	1	1	2	2	2
	II	1	0	2	0	1	2	2	2	2	0	0	0
18	I	0	0	2	0	1	1	1	2	0	0	0	1
	II	1	1	0	1	2	2	2	0	1	1	1	2
19	I	2	2	2	1	1	1	2	0	0	1	2	1
	II	0	1	0	2	0	2	0	1	1	2	0	2
20	I	1	1	1	1	1	0	2	1	2	0	0	0
	II	2	2	2	2	2	1	0	2	0	1	1	1
21	I	0	2	1	1	0	2	2	2	1	1	0	2
	II	1	0	0	1	1	0	0	0	2	2	1	0
22	I	1	2	0	1	1	1	2	0	1	0	2	0
	II	2	1	1	2	2	2	0	1	2	1	0	1
23	I	2	1	1	1	2	1	2	1	0	0	1	2
	II	1	2	2	0	1	0	0	2	1	1	2	0
24	I	0	1	2	1	1	1	2	2	2	1	2	1
	II	1	2	1	0	2	2	0	0	0	2	0	2
25	I	2	1	1	2	1	1	2	0	2	2	0	2
	II	1	2	2	1	2	2	0	1	0	0	1	0
26	I	0	1	1	1	1	0	2	1	0	2	1	1
	II	1	2	2	2	2	1	0	2	1	0	2	2
27	I	0	1	2	1	2	1	2	2	1	2	1	0
	II	1	1	0	2	1	2	0	0	2	0	2	1

Table 23:

27 choice sets, design 10.

Choice set	Alternative	D_B-error						Entropy
		Attributes						Attributes
1	I	0	1	1	1	0	1	2	2	1	0	0	1
	II	2	0	2	0	1	0	0	0	2	1	1	2
2	I	0	0	2	0	1	2	0	0	1	2	2	1
	II	1	1	0	1	0	0	1	1	2	0	0	2
3	I	0	0	2	1	2	0	0	0	2	2	0	1
	II	2	1	0	2	1	2	1	1	0	0	1	2
4	I	0	0	2	1	0	1	1	0	0	0	2	2
	II	1	2	1	0	2	0	2	1	1	1	0	0
5	I	0	1	1	0	2	2	0	2	0	0	0	0
	II	1	0	0	1	0	2	1	0	1	1	1	1
6	I	0	0	2	2	2	2	2	2	1	0	1	0
	II	1	1	0	0	0	2	0	0	2	1	2	1
7	I	0	0	0	2	1	1	0	0	0	0	1	0
	II	2	1	2	0	0	0	1	1	1	1	2	1
8	I	2	0	1	1	1	0	0	0	0	1	0	0
	II	1	2	0	0	0	1	1	1	1	2	1	1
9	I	1	0	1	0	0	1	0	2	0	1	1	2
	II	0	1	0	1	1	0	1	0	1	2	2	0
10	I	2	2	1	2	1	2	0	1	0	0	0	0
	II	1	1	2	1	2	0	0	0	0	0	0	1
11	I	1	1	1	1	2	1	1	1	2	0	1	1
	II	0	0	2	2	1	2	2	2	0	1	2	2
12	I	1	1	2	0	2	2	1	2	2	0	2	2
	II	0	2	1	1	0	0	2	0	0	1	0	0
13	I	0	0	1	0	0	1	1	0	2	1	1	0
	II	2	1	0	1	1	2	2	1	0	2	2	1
14	I	1	2	2	1	0	2	1	1	1	1	0	2
	II	0	1	1	2	1	0	2	2	2	2	1	0
15	I	0	2	1	1	1	0	1	2	0	2	2	0
	II	1	1	0	2	2	1	2	0	1	0	0	1
16	I	0	0	1	2	1	1	1	0	1	1	1	1
	II	1	1	2	1	0	2	2	1	2	2	2	2
17	I	1	0	1	1	1	2	1	1	1	2	2	2
	II	2	1	2	2	0	0	2	2	2	0	0	0
18	I	1	1	1	2	1	1	1	2	0	0	0	1
	II	0	0	0	1	2	2	2	0	1	1	1	2
19	I	0	1	1	0	1	1	2	0	0	1	2	1
	II	1	0	0	1	2	2	0	1	1	2	0	2
20	I	1	1	1	2	0	2	2	1	2	0	0	0
	II	0	2	2	0	1	1	0	2	0	1	1	1
21	I	1	1	1	0	2	1	2	2	1	1	0	2
	II	0	0	2	1	1	0	0	0	2	2	1	0
22	I	0	1	2	1	1	1	2	0	1	0	2	0
	II	1	0	1	2	2	2	0	1	2	1	0	1
23	I	1	1	1	1	1	1	2	1	0	0	1	2
	II	2	2	2	2	0	2	0	2	1	1	2	0
24	I	1	1	1	1	0	1	2	2	2	1	2	1
	II	0	1	0	2	1	2	0	0	0	2	0	2
25	I	1	1	1	1	0	2	2	0	2	2	0	2
	II	2	2	2	0	1	0	0	1	0	0	1	0
26	I	2	1	1	0	1	2	2	1	0	2	1	1
	II	1	2	2	2	2	1	0	2	1	0	2	2
27	I	1	1	1	2	1	1	2	2	1	2	1	0
	II	0	2	0	0	0	2	0	0	2	0	2	1

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Published Online: 2016-4-30

Published in Print: 2016-6-1

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https://doi.org/10.1515/roms-2014-0002

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semi-parametric semi-Bayesian mixed logit design; heterogeneity; estimation accuracy; multinomial logit design; D-optimality; entropy