Julian Sagebiel
Often we assume a data generating process that aligns with the standard models we use for analysis
Random utility model with Gumbel iid errors
Unobserved preference heterogeneity
Still, we know that the idea of RUM respondents is quite unrealistic
There are good reasons to use RUM
It is convenient
It may be a sufficiently good approximation
It allows welfare calculations
Brainstorming: Gather some ideas of potential violations of RUM based models
In RUM, we would assume the following utility function
\[ U = \beta X + \epsilon \]
Attribute Non Attendence (no MRS)
Elimination by aspects
Purely lexiographic preferences
Left-Right Bias
Loss aversion
Key question: How do RUM models perform if the data is not RUM
A DGP is the way how data is created.
Sunflower Height=Amount of Sunlight+Water+Soil Nutrients+Random Growth Factor
We never know the right DGP, we can only approximate it
Any statistical model is based on a DGP
A model is a strong simplification of a real phenomenon
A choice model is a strong simplification of how people make choices (i.e. the DGP)
Using a conditional logit model implies a precise definition of the DGP
The model is not more or not less than our assumptions on the DGP
\[ U = \beta X + \epsilon \]
Estimating a RUM usually gives us some statistically significant results
If people do not apply to RUM, our results may get biased.
The following model is estimated from the feed additives choice experiment
What does the regression table tell us about the DGP and potential deviations of RUM?
| Model 1 | |
|---|---|
| basc | 0.17 (0.04)*** |
| bcow | 0.29 (0.02)*** |
| badv | 0.32 (0.02)*** |
| bvet | 0.32 (0.02)*** |
| bfar | 0.27 (0.02)*** |
| bmet | 0.18 (0.01)*** |
| bbon | 0.37 (0.01)*** |
| No Observations | 28800 |
| No Respondents | 3600 |
| Log Likelihood (Null) | -31640.03 |
| Log Likelihood (Converged) | -20401.99 |
Question to all: If you are a reviewer and see these results, would you have any doubts?
To get a better idea, lets look at some choices
The following table is just a few respondents
Can you see anything in the data?
| ID | Choice_situation | alt1_cow | alt1_adv | alt1_vet | alt1_far | alt1_met | alt1_bon | alt2_cow | alt2_adv | alt2_vet | alt2_far | alt2_met | alt2_bon | CHOICE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 2162 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 2882 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 2 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 1 |
| 2162 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 3 |
| 2882 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 1 |
| 2 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 |
| 2162 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 |
| 2882 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 |
| 1 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 |
| 2161 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 |
| 2881 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 2 |
| 2 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 |
| 2162 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 1 |
| 2882 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 |
| 2 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 1 |
| 2162 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 |
| 2882 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 |
| 1 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 2 |
| 2161 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 |
| 2881 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 2 |
| 1 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 2 |
| 2161 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 2 |
| 2881 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 2 |
| 1 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 |
| 2161 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 |
| 2881 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 3 |
| 2 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 1 |
| 2162 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 1 |
| 2882 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 1 |
| 2 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 |
| 2162 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 |
| 2882 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 |
| 1 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 |
| 2161 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 |
| 2881 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 |
| 1 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 |
| 2161 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 |
| 2881 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 |
| 1 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 |
| 2161 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 |
| 2881 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 2 |
| 2 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 1 |
| 2162 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 |
| 2882 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 1 |
| 1 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 2 |
| 2161 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 |
| 2881 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 2 |
The data we just looked at are simulated data
Simulations give us full control over the data generating process (DGP)
The data was simulated using different decision heuristics
As the data is simulated, we know the correct DGP and thus if the model is correct or not
| ID | Choice_situation | alt1_cow | alt1_adv | alt1_vet | alt1_far | alt1_met | alt1_bon | alt2_cow | alt2_adv | alt2_vet | alt2_far | alt2_met | alt2_bon | Block | group | V_1 | V_2 | V_3 | e_1 | e_2 | e_3 | U_1 | U_2 | U_3 | CHOICE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 1.2606303 | -0.0001064 | 0.4438955 | 2.7606303 | 1.7998936 | 0.6438955 | 1 |
| 1 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.2663207 | 0.6080929 | -1.1184641 | 2.3663207 | 2.4080929 | -0.9184641 | 2 |
| 1 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 1.5130251 | 1.0353377 | -0.1032120 | 3.3130251 | 4.3353377 | 0.0967880 | 2 |
| 1 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | 1.0994573 | -0.8836217 | -1.0041691 | 2.2994573 | 0.0163783 | -0.8041691 | 1 |
| 1 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 2.6612205 | 0.8030552 | -0.6974163 | 5.3612205 | 2.9030552 | -0.4974163 | 1 |
| 1 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 2.8531287 | 0.1904686 | 0.7794196 | 4.3531287 | 1.9904686 | 0.9794196 | 1 |
| 1 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 0.0742271 | 0.5877955 | -0.7728690 | 3.0742271 | 2.9877955 | -0.5728690 | 1 |
| 1 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | 1.1556488 | 0.7101979 | -0.1524561 | 3.5556488 | 4.0101979 | 0.0475439 | 2 |
| 2 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 0.8530360 | 0.0108760 | 0.8482966 | 4.4530360 | 0.9108760 | 1.0482966 | 1 |
| 2 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 1.0629435 | 1.4820326 | -0.1926237 | 3.7629435 | 2.6820326 | 0.0073763 | 1 |
| 2 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | -0.7359799 | -1.3557277 | 0.9440878 | 0.4640201 | 1.9442723 | 1.1440878 | 2 |
| 2 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 0.4510422 | 0.6350862 | 2.6084106 | 2.5510422 | 3.6350862 | 2.8084106 | 2 |
| 2 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 3.7227908 | 0.2203160 | 0.7968505 | 5.2227908 | 2.3203160 | 0.9968505 | 1 |
| 2 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | -0.1005443 | -1.1628394 | -0.3342054 | 2.2994557 | -0.2628394 | -0.1342054 | 1 |
| 2 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.6700349 | 1.6353508 | 1.3852486 | 1.5700349 | 4.3353508 | 1.5852486 | 2 |
| 2 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | -1.1075404 | -0.4046616 | 1.1858642 | 1.8924596 | 1.6953384 | 1.3858642 | 1 |
| 3 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.8678303 | 0.5826661 | -0.2255671 | 0.6321697 | 2.3826661 | -0.0255671 | 2 |
| 3 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.6483179 | -1.3844568 | 1.2320727 | 2.7483179 | 0.4155432 | 1.4320727 | 1 |
| 3 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 0.7359145 | 0.0371263 | -0.9898015 | 2.5359145 | 3.3371263 | -0.7898015 | 2 |
| 3 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -0.3453707 | 1.8019234 | -0.1438140 | 0.8546293 | 2.7019234 | 0.0561860 | 2 |
| 3 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 1.1001233 | 0.7355253 | 0.3302873 | 3.8001233 | 2.8355253 | 0.5302873 | 1 |
| 3 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.5198692 | 0.6109552 | -1.1900497 | 0.9801308 | 2.4109552 | -0.9900497 | 2 |
| 3 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 4.6170242 | -0.2357096 | -0.3531038 | 7.6170242 | 2.1642904 | -0.1531038 | 1 |
| 3 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | 0.3302260 | 0.0131924 | 0.2629378 | 2.7302260 | 3.3131924 | 0.4629378 | 2 |
| 4 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 0.1182670 | 2.5395730 | 3.2915101 | 3.7182670 | 3.4395730 | 3.4915101 | 1 |
| 4 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 1.8658662 | 0.1989536 | 0.3159225 | 4.5658662 | 1.3989536 | 0.5159225 | 1 |
| 4 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 1.1832195 | -1.2572051 | 3.2006742 | 2.3832195 | 2.0427949 | 3.4006742 | 3 |
| 4 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 2.6885540 | 1.3173080 | -0.2843732 | 4.7885540 | 4.3173080 | -0.0843732 | 1 |
| 4 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | -0.8023013 | 1.4371628 | 0.1593705 | 0.6976987 | 3.5371628 | 0.3593705 | 2 |
| 4 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 1.2489432 | 4.2182805 | 0.7173716 | 3.6489432 | 5.1182805 | 0.9173716 | 2 |
| 4 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.1858225 | 0.4456220 | 0.2780780 | 1.0858225 | 3.1456220 | 0.4780780 | 2 |
| 4 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 0.5343423 | 1.1190677 | -0.5519986 | 3.5343423 | 3.2190677 | -0.3519986 | 1 |
| 5 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.1479072 | -0.1122433 | 2.0039114 | 1.3520928 | 1.6877567 | 2.2039114 | 3 |
| 5 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | -0.7589834 | -0.9571965 | 0.5809490 | 1.3410166 | 0.8428035 | 0.7809490 | 1 |
| 5 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 0.1044386 | 1.8715922 | -0.5523303 | 1.9044386 | 5.1715922 | -0.3523303 | 2 |
| 5 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -1.4007410 | 0.2591963 | 0.8259824 | -0.2007410 | 1.1591963 | 1.0259824 | 2 |
| 5 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 0.3666695 | 1.3490850 | -0.0366271 | 3.0666695 | 3.4490850 | 0.1633729 | 2 |
| 5 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | -1.0621769 | -0.6435810 | -1.2998089 | 0.4378231 | 1.1564190 | -1.0998089 | 2 |
| 5 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 0.3114798 | 1.0910527 | 1.4335898 | 3.3114798 | 3.4910527 | 1.6335898 | 2 |
| 5 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -0.9292686 | -0.7806398 | 0.9467055 | 1.4707314 | 2.5193602 | 1.1467055 | 2 |
| 6 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | -1.2044700 | 0.8835375 | 1.1245905 | 2.3955300 | 1.7835375 | 1.3245905 | 1 |
| 6 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 6.3959437 | 1.8164732 | -1.6435748 | 9.0959437 | 3.0164732 | -1.4435748 | 1 |
| 6 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 1.8430660 | 2.1483922 | -0.4963695 | 3.0430660 | 5.4483922 | -0.2963695 | 2 |
| 6 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | -0.4881596 | 5.6415180 | 1.4593814 | 1.6118404 | 8.6415180 | 1.6593814 | 2 |
| 6 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | -1.2633638 | -0.5403731 | 1.3670424 | 0.2366362 | 1.5596269 | 1.5670424 | 3 |
| 6 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 1.1766784 | 0.3423929 | 0.0161535 | 3.5766784 | 1.2423929 | 0.2161535 | 1 |
| 6 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.4126669 | -1.2747480 | -1.5636682 | 1.3126669 | 1.4252520 | -1.3636682 | 2 |
| 6 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | -0.7363453 | 1.1162124 | -0.4699908 | 2.2636547 | 3.2162124 | -0.2699908 | 2 |
| 7 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 0.9653491 | 1.1158550 | -0.7901764 | 2.4653491 | 2.9158550 | -0.5901764 | 2 |
| 7 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 3.6893566 | 0.5624485 | -0.2221840 | 5.7893566 | 2.3624485 | -0.0221840 | 1 |
| 7 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | -0.4879056 | 3.5847796 | -1.3237347 | 1.3120944 | 6.8847796 | -1.1237347 | 2 |
| 7 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | 0.8165038 | 2.6743297 | 0.9992979 | 2.0165038 | 3.5743297 | 1.1992979 | 2 |
| 7 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | -0.0311807 | -0.6339399 | -0.2614249 | 2.6688193 | 1.4660601 | -0.0614249 | 1 |
| 7 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 0.0844100 | -1.5491443 | -0.4829470 | 1.5844100 | 0.2508557 | -0.2829470 | 1 |
| 7 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 0.5885939 | -0.2695084 | 1.8439330 | 3.5885939 | 2.1304916 | 2.0439330 | 1 |
| 7 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -1.8267379 | 0.3913881 | 1.0266739 | 0.5732621 | 3.6913881 | 1.2266739 | 2 |
| 8 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 0.2146311 | 3.0537811 | 0.4380427 | 3.8146311 | 3.9537811 | 0.6380427 | 2 |
| 8 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 2.0977653 | 0.7149544 | -0.8744680 | 4.7977653 | 1.9149544 | -0.6744680 | 1 |
| 8 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 0.1544896 | 0.6783032 | 2.7279251 | 1.3544896 | 3.9783032 | 2.9279251 | 2 |
| 8 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 0.9951714 | -1.1309307 | 1.0282519 | 3.0951714 | 1.8690693 | 1.2282519 | 1 |
| 8 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 0.1404234 | -0.4443173 | 1.6142149 | 1.6404234 | 1.6556827 | 1.8142149 | 3 |
| 8 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 0.9250596 | 2.3320759 | 1.3967575 | 3.3250596 | 3.2320759 | 1.5967575 | 1 |
| 8 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 1.9428024 | 2.1920130 | 1.0502366 | 2.8428024 | 4.8920130 | 1.2502366 | 2 |
| 8 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 0.6359381 | -0.5364219 | 1.3727514 | 3.6359381 | 1.5635781 | 1.5727514 | 1 |
| 9 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 1.1706317 | 0.7692809 | 1.9345501 | 2.6706317 | 2.5692809 | 2.1345501 | 1 |
| 9 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.2212748 | 1.0374326 | -0.2779420 | 2.3212748 | 2.8374326 | -0.0779420 | 2 |
| 9 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 0.4676582 | 1.9664472 | 0.0234001 | 2.2676582 | 5.2664472 | 0.2234001 | 2 |
| 9 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -0.5921694 | 3.3713295 | 0.2438945 | 0.6078306 | 4.2713295 | 0.4438945 | 2 |
| 9 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | -0.5150756 | -0.7085529 | 2.7736114 | 2.1849244 | 1.3914471 | 2.9736114 | 3 |
| 9 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 1.4361750 | -0.7134323 | 0.3206485 | 2.9361750 | 1.0865677 | 0.5206485 | 1 |
| 9 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 1.5673228 | -0.1422197 | 1.8140208 | 4.5673228 | 2.2577803 | 2.0140208 | 1 |
| 9 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -1.0005401 | 1.6881335 | 0.6345433 | 1.3994599 | 4.9881335 | 0.8345433 | 2 |
| 10 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | -1.3840494 | 3.4267966 | 0.1517616 | 2.2159506 | 4.3267966 | 0.3517616 | 2 |
| 10 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 0.3849055 | 1.6268282 | 2.0031301 | 3.0849055 | 2.8268282 | 2.2031301 | 1 |
| 10 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 0.8181420 | -0.0641513 | 0.6330116 | 2.0181420 | 3.2358487 | 0.8330116 | 2 |
| 10 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | -0.4895110 | 1.0550499 | 0.3833172 | 1.6104890 | 4.0550499 | 0.5833172 | 2 |
| 10 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 0.5126866 | -0.0090890 | 3.2630820 | 2.0126866 | 2.0909110 | 3.4630820 | 3 |
| 10 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 1.9876511 | 0.4168428 | 1.2407532 | 4.3876511 | 1.3168428 | 1.4407532 | 1 |
| 10 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.0757268 | 0.3020574 | -1.1795159 | 0.9757268 | 3.0020574 | -0.9795159 | 2 |
| 10 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | -1.1511680 | 0.8399190 | -0.9910629 | 1.8488320 | 2.9399190 | -0.7910629 | 2 |
| 11 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 0.9282458 | 0.0232414 | 1.5506934 | 2.4282458 | 1.8232414 | 1.7506934 | 1 |
| 11 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 1.3607399 | -0.4737274 | 0.1729479 | 3.4607399 | 1.3262726 | 0.3729479 | 1 |
| 11 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 1.3973782 | -0.1890841 | -0.5690359 | 3.1973782 | 3.1109159 | -0.3690359 | 1 |
| 11 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -0.9596717 | 0.8572310 | -0.1812751 | 0.2403283 | 1.7572310 | 0.0187249 | 2 |
| 11 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | -0.1112423 | 0.4320758 | 0.8665942 | 2.5887577 | 2.5320758 | 1.0665942 | 1 |
| 11 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 1.4082259 | -0.1406057 | -0.4491501 | 2.9082259 | 1.6593943 | -0.2491501 | 1 |
| 11 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 0.8287018 | 0.4779937 | -0.2796278 | 3.8287018 | 2.8779937 | -0.0796278 | 1 |
| 11 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | 1.1337371 | 0.0813474 | 2.6823146 | 3.5337371 | 3.3813474 | 2.8823146 | 1 |
| 12 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 0.2744547 | 1.9491903 | 0.5279599 | 3.8744547 | 2.8491903 | 0.7279599 | 1 |
| 12 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 0.9424685 | -0.1499867 | -0.5220195 | 3.6424685 | 1.0500133 | -0.3220195 | 1 |
| 12 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 0.9921861 | 0.7232335 | 2.3452723 | 2.1921861 | 4.0232335 | 2.5452723 | 2 |
| 12 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 1.9371476 | -1.2097155 | 0.5177815 | 4.0371476 | 1.7902845 | 0.7177815 | 1 |
| 12 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 2.8230491 | 2.9873047 | 1.4771512 | 4.3230491 | 5.0873047 | 1.6771512 | 2 |
| 12 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 0.1656205 | 1.6004518 | -0.0609233 | 2.5656205 | 2.5004518 | 0.1390767 | 1 |
| 12 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | -0.1083923 | 1.4698743 | 0.9353046 | 0.7916077 | 4.1698743 | 1.1353046 | 2 |
| 12 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 0.9548782 | 1.3429298 | 1.9045229 | 3.9548782 | 3.4429298 | 2.1045229 | 1 |
| 13 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.8056778 | -0.2856111 | -0.3927758 | 0.6943222 | 1.5143889 | -0.1927758 | 2 |
| 13 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.2802507 | 1.1692328 | -0.1666276 | 2.3802507 | 2.9692328 | 0.0333724 | 2 |
| 13 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | -0.3084121 | 1.9530998 | -0.7567399 | 1.4915879 | 5.2530998 | -0.5567399 | 2 |
| 13 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | 0.5556699 | 0.0319981 | 1.6216316 | 1.7556699 | 0.9319981 | 1.8216316 | 3 |
| 13 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 0.1452410 | 1.9370333 | 0.9433656 | 2.8452410 | 4.0370333 | 1.1433656 | 2 |
| 13 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | -1.8146722 | 0.7953156 | -0.1613881 | -0.3146722 | 2.5953156 | 0.0386119 | 2 |
| 13 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | -1.1733101 | 0.0526088 | 0.8399431 | 1.8266899 | 2.4526088 | 1.0399431 | 2 |
| 13 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | 0.1448206 | 0.2348710 | -0.2917286 | 2.5448206 | 3.5348710 | -0.0917286 | 2 |
| 14 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 2.9195735 | 2.3342955 | -1.1718776 | 6.5195735 | 3.2342955 | -0.9718776 | 1 |
| 14 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | -0.6677045 | 0.9097239 | -0.1673405 | 2.0322955 | 2.1097239 | 0.0326595 | 2 |
| 14 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 0.3283862 | -0.2843285 | 1.2265154 | 1.5283862 | 3.0156715 | 1.4265154 | 2 |
| 14 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | -0.5521096 | -0.1646452 | -0.4803340 | 1.5478904 | 2.8353548 | -0.2803340 | 2 |
| 14 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 0.8036367 | 0.7639964 | 0.2947557 | 2.3036367 | 2.8639964 | 0.4947557 | 2 |
| 14 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 0.2712418 | 2.6402984 | 0.3438280 | 2.6712418 | 3.5402984 | 0.5438280 | 2 |
| 14 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.6655475 | 0.0852692 | 0.4024220 | 1.5655475 | 2.7852692 | 0.6024220 | 2 |
| 14 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | -0.4189039 | 0.8337069 | 0.8619900 | 2.5810961 | 2.9337069 | 1.0619900 | 2 |
| 15 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 3.3662310 | -1.0742352 | -0.5117387 | 4.8662310 | 0.7257648 | -0.3117387 | 1 |
| 15 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.4008935 | 1.5207797 | 0.4983802 | 2.5008935 | 3.3207797 | 0.6983802 | 2 |
| 15 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 0.9260945 | -0.6222102 | -0.9271397 | 2.7260945 | 2.6777898 | -0.7271397 | 1 |
| 15 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -0.5243619 | 1.8711494 | 2.8309415 | 0.6756381 | 2.7711494 | 3.0309415 | 3 |
| 15 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | -0.7616209 | 0.3573748 | 1.8320659 | 1.9383791 | 2.4573748 | 2.0320659 | 2 |
| 15 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 0.1266627 | 2.2123202 | 0.5994242 | 1.6266627 | 4.0123202 | 0.7994242 | 2 |
| 15 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | -0.0121946 | -0.6035430 | -0.1161679 | 2.9878054 | 1.7964570 | 0.0838321 | 1 |
| 15 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -1.5845099 | 2.6305392 | 2.3345019 | 0.8154901 | 5.9305392 | 2.5345019 | 2 |
| 16 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | -0.3738873 | -0.9089386 | -0.5736057 | 3.2261127 | -0.0089386 | -0.3736057 | 1 |
| 16 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 0.5988429 | 1.0705506 | 1.6749715 | 3.2988429 | 2.2705506 | 1.8749715 | 1 |
| 16 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 2.1800982 | 1.3332032 | -1.3003579 | 3.3800982 | 4.6332032 | -1.1003579 | 2 |
| 16 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 0.2012731 | 0.4369876 | 1.6261076 | 2.3012731 | 3.4369876 | 1.8261076 | 2 |
| 16 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | -0.2573656 | 2.0787436 | 1.2784146 | 1.2426344 | 4.1787436 | 1.4784146 | 2 |
| 16 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 1.3139167 | -1.1542511 | 2.3183794 | 3.7139167 | -0.2542511 | 2.5183794 | 1 |
| 16 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | -0.9480991 | -1.0181748 | 3.5557648 | -0.0480991 | 1.6818252 | 3.7557648 | 3 |
| 16 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 1.8565630 | -0.1660831 | -0.3234651 | 4.8565630 | 1.9339169 | -0.1234651 | 1 |
| 17 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | -1.0977826 | -0.3404461 | -0.4008508 | 0.4022174 | 1.4595539 | -0.2008508 | 2 |
| 17 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 3.1974096 | 2.0592356 | 3.0874854 | 5.2974096 | 3.8592356 | 3.2874854 | 1 |
| 17 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | -1.8217673 | 0.4812280 | -1.2865181 | -0.0217673 | 3.7812280 | -1.0865181 | 2 |
| 17 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -0.1881533 | 0.6361656 | 0.8144051 | 1.0118467 | 1.5361656 | 1.0144051 | 2 |
| 17 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 1.8219571 | -0.7370248 | -0.3671571 | 4.5219571 | 1.3629752 | -0.1671571 | 1 |
| 17 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 1.4997066 | -0.8101609 | 0.8319353 | 2.9997066 | 0.9898391 | 1.0319353 | 1 |
| 17 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | -1.4223804 | -0.0060769 | 0.5832801 | 1.5776196 | 2.3939231 | 0.7832801 | 2 |
| 17 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | 0.3769516 | 1.8240718 | -0.4550739 | 2.7769516 | 5.1240718 | -0.2550739 | 2 |
| 18 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 2.0155549 | 1.5512555 | 2.1012230 | 5.6155549 | 2.4512555 | 2.3012230 | 1 |
| 18 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 1.0485523 | -0.4324169 | -0.7062930 | 3.7485523 | 0.7675831 | -0.5062930 | 1 |
| 18 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 0.7915597 | -0.1261139 | 1.5728713 | 1.9915597 | 3.1738861 | 1.7728713 | 2 |
| 18 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 0.3270647 | -0.3650944 | 0.9667361 | 2.4270647 | 2.6349056 | 1.1667361 | 2 |
| 18 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | -1.7650271 | 1.1411943 | 0.7593768 | -0.2650271 | 3.2411943 | 0.9593768 | 2 |
| 18 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 0.1624004 | -0.1229293 | 0.3440701 | 2.5624004 | 0.7770707 | 0.5440701 | 1 |
| 18 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | -0.2408775 | -0.5623836 | 0.2683309 | 0.6591225 | 2.1376164 | 0.4683309 | 2 |
| 18 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 1.1126180 | 4.7210839 | 1.8612242 | 4.1126180 | 6.8210839 | 2.0612242 | 2 |
| 19 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.4343847 | -0.1149750 | 0.5250572 | 1.0656153 | 1.6850250 | 0.7250572 | 2 |
| 19 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.4024674 | 0.4119786 | 1.2110419 | 2.5024674 | 2.2119786 | 1.4110419 | 1 |
| 19 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | -0.9273641 | 2.4527016 | 1.8341532 | 0.8726359 | 5.7527016 | 2.0341532 | 2 |
| 19 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | -0.2324014 | 1.1450453 | 1.3187159 | 0.9675986 | 2.0450453 | 1.5187159 | 2 |
| 19 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 0.1785370 | -0.8792794 | 0.2099514 | 2.8785370 | 1.2207206 | 0.4099514 | 1 |
| 19 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.1566453 | 0.3628500 | 0.5262657 | 1.3433547 | 2.1628500 | 0.7262657 | 2 |
| 19 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 1.6552150 | -0.4109460 | -0.0047152 | 4.6552150 | 1.9890540 | 0.1952848 | 1 |
| 19 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -1.0089813 | 1.7677465 | -0.3999686 | 1.3910187 | 5.0677465 | -0.1999686 | 2 |
| 20 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | -0.0896211 | 2.6858677 | 0.5622052 | 3.5103789 | 3.5858677 | 0.7622052 | 2 |
| 20 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | -0.8759458 | 0.0645036 | 0.0777809 | 1.8240542 | 1.2645036 | 0.2777809 | 1 |
| 20 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | -1.2208761 | -1.0737197 | -0.2418767 | -0.0208761 | 2.2262803 | -0.0418767 | 2 |
| 20 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | -0.1879346 | -1.3174244 | -0.5396619 | 1.9120654 | 1.6825756 | -0.3396619 | 1 |
| 20 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 1.9705007 | -0.5844581 | -0.0885146 | 3.4705007 | 1.5155419 | 0.1114854 | 1 |
| 20 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 3.5131277 | 3.4063755 | 1.5950800 | 5.9131277 | 4.3063755 | 1.7950800 | 1 |
| 20 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 1.7915652 | -1.6519993 | 1.7995446 | 2.6915652 | 1.0480007 | 1.9995446 | 1 |
| 20 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 1.4305241 | 1.4802242 | 0.2895619 | 4.4305241 | 3.5802242 | 0.4895619 | 1 |
| 21 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 0.5188243 | 0.0668446 | 0.0098922 | 2.0188243 | 1.8668446 | 0.2098922 | 1 |
| 21 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | -0.5777947 | -1.0934556 | 1.2265592 | 1.5222053 | 0.7065444 | 1.4265592 | 1 |
| 21 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | -0.7175084 | 0.9790226 | 1.9289591 | 1.0824916 | 4.2790226 | 2.1289591 | 2 |
| 21 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | 0.8034195 | 0.0541033 | -0.5460703 | 2.0034195 | 0.9541033 | -0.3460703 | 1 |
| 21 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | -0.7673433 | 4.0229858 | 3.1984928 | 1.9326567 | 6.1229858 | 3.3984928 | 2 |
| 21 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | -1.5733257 | 0.3840076 | -0.4517147 | -0.0733257 | 2.1840076 | -0.2517147 | 2 |
| 21 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 1.4148579 | -0.4140772 | 0.6351006 | 4.4148579 | 1.9859228 | 0.8351006 | 1 |
| 21 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -0.7754695 | 2.7113716 | -0.2856749 | 1.6245305 | 6.0113716 | -0.0856749 | 2 |
| 22 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 1.3838974 | -0.3356571 | 0.5537056 | 4.9838974 | 0.5643429 | 0.7537056 | 1 |
| 22 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | -0.6389404 | 1.4495835 | 0.4080598 | 2.0610596 | 2.6495835 | 0.6080598 | 2 |
| 22 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 2.3266369 | 0.7400508 | 1.3271600 | 3.5266369 | 4.0400508 | 1.5271600 | 2 |
| 22 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 0.9623242 | 0.2256843 | 0.7406459 | 3.0623242 | 3.2256843 | 0.9406459 | 2 |
| 22 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 0.5528150 | -0.4985173 | -0.1733400 | 2.0528150 | 1.6014827 | 0.0266600 | 1 |
| 22 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 0.6768319 | -0.0740796 | 1.5270424 | 3.0768319 | 0.8259204 | 1.7270424 | 1 |
| 22 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.3764531 | -0.5842859 | -0.9676926 | 1.2764531 | 2.1157141 | -0.7676926 | 2 |
| 22 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | -0.1156253 | 0.0092832 | 0.9547435 | 2.8843747 | 2.1092832 | 1.1547435 | 1 |
| 23 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | 2.1150525 | -0.0501334 | 0.3169699 | 3.6150525 | 1.7498666 | 0.5169699 | 1 |
| 23 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 0.4304851 | 0.8093394 | -1.4509626 | 2.5304851 | 2.6093394 | -1.2509626 | 2 |
| 23 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | -1.1341497 | -0.9246697 | -0.0148908 | 0.6658503 | 2.3753303 | 0.1851092 | 2 |
| 23 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | 0.3188452 | -0.8388149 | 0.5028024 | 1.5188452 | 0.0611851 | 0.7028024 | 1 |
| 23 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | -0.1011105 | -0.1872467 | -0.6401751 | 2.5988895 | 1.9127533 | -0.4401751 | 1 |
| 23 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 6.4338041 | 0.1311793 | 0.0552560 | 7.9338041 | 1.9311793 | 0.2552560 | 1 |
| 23 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 0.3714764 | -0.1609574 | -0.4877071 | 3.3714764 | 2.2390426 | -0.2877071 | 1 |
| 23 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | 1.2949188 | 2.8480000 | 0.7783896 | 3.6949188 | 6.1480000 | 0.9783896 | 2 |
| 24 | 1 | 0 | 1 | 1 | 1 | 3 | 6 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 3.6 | 0.9 | 0.2 | 1.1361060 | -0.6125712 | -1.0794398 | 4.7361060 | 0.2874288 | -0.8794398 | 1 |
| 24 | 2 | 1 | 0 | 0 | 1 | 0 | 7 | 0 | 1 | 0 | 0 | 1 | 2 | 2 | 1 | 2.7 | 1.2 | 0.2 | 0.4627792 | -0.8500202 | 0.8204245 | 3.1627792 | 0.3499798 | 1.0204245 | 1 |
| 24 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 3 | 5 | 2 | 1 | 1.2 | 3.3 | 0.2 | 0.7799443 | -0.0064863 | 0.6145697 | 1.9799443 | 3.2935137 | 0.8145697 | 2 |
| 24 | 5 | 0 | 0 | 1 | 0 | 2 | 4 | 0 | 1 | 0 | 1 | 1 | 7 | 2 | 1 | 2.1 | 3.0 | 0.2 | 0.8027735 | 0.3090594 | 0.9312733 | 2.9027735 | 3.3090594 | 1.1312733 | 2 |
| 24 | 6 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 5 | 2 | 1 | 1.5 | 2.1 | 0.2 | 0.2715031 | -0.8831655 | -0.1993149 | 1.7715031 | 1.2168345 | 0.0006851 | 1 |
| 24 | 10 | 1 | 1 | 1 | 0 | 1 | 4 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2.4 | 0.9 | 0.2 | 1.1804119 | 2.2918195 | -0.2871011 | 3.5804119 | 3.1918195 | -0.0871011 | 1 |
| 24 | 11 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 4 | 2 | 1 | 0.9 | 2.7 | 0.2 | 0.6324759 | 1.6886296 | -0.5010965 | 1.5324759 | 4.3886296 | -0.3010965 | 2 |
| 24 | 15 | 0 | 0 | 0 | 0 | 3 | 7 | 1 | 1 | 1 | 1 | 0 | 3 | 2 | 1 | 3.0 | 2.1 | 0.2 | 0.7000821 | 1.9812950 | 0.7678483 | 3.7000821 | 4.0812950 | 0.9678483 | 2 |
| 25 | 4 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 1 | 0 | 0 | 2 | 3 | 1 | 1 | 1.5 | 1.8 | 0.2 | -0.2936195 | 1.0797569 | 0.4001707 | 1.2063805 | 2.8797569 | 0.6001707 | 2 |
| 25 | 7 | 1 | 0 | 1 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 4 | 1 | 1 | 2.1 | 1.8 | 0.2 | 4.1840236 | 0.4616781 | 2.6931134 | 6.2840236 | 2.2616781 | 2.8931134 | 1 |
| 25 | 8 | 0 | 0 | 0 | 1 | 0 | 5 | 0 | 1 | 1 | 0 | 2 | 7 | 1 | 1 | 1.8 | 3.3 | 0.2 | 1.0122236 | 0.2287786 | -0.1228385 | 2.8122236 | 3.5287786 | 0.0771615 | 2 |
| 25 | 9 | 1 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1.2 | 0.9 | 0.2 | 0.6942845 | 0.1088424 | -0.3769196 | 1.8942845 | 1.0088424 | -0.1769196 | 1 |
| 25 | 12 | 1 | 1 | 0 | 0 | 1 | 6 | 1 | 0 | 1 | 1 | 3 | 1 | 1 | 1 | 2.7 | 2.1 | 0.2 | 1.0029091 | -0.9149497 | -1.8987643 | 3.7029091 | 1.1850503 | -1.6987643 | 1 |
| 25 | 13 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 3 | 1 | 1 | 1 | 1.5 | 1.8 | 0.2 | 1.1353083 | 2.7187466 | -0.2560346 | 2.6353083 | 4.5187466 | -0.0560346 | 2 |
| 25 | 14 | 1 | 1 | 0 | 1 | 2 | 5 | 1 | 0 | 1 | 0 | 0 | 6 | 1 | 1 | 3.0 | 2.4 | 0.2 | 1.5448817 | 4.7223123 | 0.0382135 | 4.5448817 | 7.1223123 | 0.2382135 | 2 |
| 25 | 16 | 0 | 1 | 1 | 0 | 3 | 3 | 1 | 0 | 1 | 1 | 2 | 6 | 1 | 1 | 2.4 | 3.3 | 0.2 | -1.0505700 | -1.4655248 | -0.3838638 | 1.3494300 | 1.8344752 | -0.1838638 | 2 |
In the data there are three different DGPs
Group 1 (60%): RUM (\(\alpha=0.2\) and all \(\beta=0.3\))
\[ U = \alpha + \beta_{cow}\text{cow}+\beta_{adv}\text{adv} + \beta_{vet}\text{vet} + \\ \beta_{far}\text{far}+\beta_{met}\text{met}+\beta_{bon}\text{bon} + \epsilon\]
\[ U = \alpha + \beta_{cow}\text{cow}+\beta_{adv}\text{adv} + \beta_{vet}\text{vet} + \beta_{far}\text{far}+\beta_{bon}\text{bon} + \epsilon\]
\[ U = \beta_{bon2}\text{bon} + \epsilon\]
As we know the DGP, we can estimate models for each group and compare results to the full model
In reality, however we do not know this
Lets see if there is a problem
There are separate html files that give for each choice set the choice frequencies
| ALL | RUM | NonAttendence | Price | |
|---|---|---|---|---|
| basc | 0.17 (0.04)*** | 0.28 (0.05)*** | 0.17 (0.06)** | 0.52 (0.75) |
| bcow | 0.29 (0.02)*** | 0.33 (0.02)*** | 0.27 (0.04)*** | -0.05 (0.10) |
| badv | 0.32 (0.02)*** | 0.31 (0.02)*** | 0.37 (0.03)*** | -0.96 (1.07) |
| bvet | 0.32 (0.02)*** | 0.31 (0.02)*** | 0.33 (0.04)*** | -1.00 (1.13) |
| bfar | 0.27 (0.02)*** | 0.29 (0.02)*** | 0.31 (0.03)*** | -0.04 (0.07) |
| bmet | 0.18 (0.01)*** | 0.32 (0.01)*** | 0.00 (0.01) | 0.48 (0.33) |
| bbon | 0.37 (0.01)*** | 0.31 (0.01)*** | 0.28 (0.01)*** | 2.72 (0.76)*** |
| No Observations | 28800 | 17280 | 5760 | 5760 |
| No Respondents | 3600 | 2160 | 720 | 720 |
| Log Likelihood (Null) | -31640.03 | -18984.02 | -6328.01 | -6328.01 |
| Log Likelihood (Converged) | -20401.99 | -12884.39 | -4817.40 | -611.21 |
We may try a latent class model to detect heuristics
In the ideal case, we would find two classes of about 20 % and one class with about 60%
The classes would reflect the DGP in the three groups
| Class 1: 15% | Class 2: 20% | Class 3: 65% | |
|---|---|---|---|
| basc | 0.35 (0.13)** | -17.01 (9.81)* | -0.03 (0.01)*** |
| bcow | 0.09 (0.06) | -0.21 (0.07)** | 0.37 (0.03)*** |
| badv | -0.31 (0.21) | -15.47 (9.75) | 0.31 (0.03)*** |
| bvet | -0.23 (0.16) | -7.75 (7.61) | 0.15 (0.02)*** |
| bfar | -0.23 (0.34) | -7.75 (3.83)* | 0.14 (0.02)*** |
| bmet | 0.66 (0.14)*** | 8.21 (4.85)* | 0.15 (0.03)*** |
| bbon | 0.33 (0.03)*** | 18.04 (9.72)* | 0.29 (0.01)*** |
| No Observations | 28800 | ||
| No Respondents | 3600 | ||
| Log Likelihood (Null) | -31640.03 | ||
| Log Likelihood (Converged) | -19918.67 |
Heuristics are likely present in the DGP
Presence of heuristics violates standard RUM modelling
Not accounting for heuristics can lead to biases
How severe the biases are depends
Latent class models are not necessarily useful
Check the data manually
Try to identify respondents who apply some standard heuristics
Identifying respondents who only regard one attribute may be easy
Attribute Non attendence models may help as well (see tomorrow)
You find the dataset feedadd_data_practice.RDSin the folder data
Have a look at the data and try to identify heuristics by either looking at choice frequencies or estimated models
Estimate a four class LC model
Try to write code that identifies a Bonus heuristic

Biases and Heuristics