This vignette shows how to reproduce every table, graph and test from Külpmann and Kuzmics (2020).
The data as well as predictions for each theory mentioned in Külpmann and Kuzmics (2020) are included as additional data to the package “oottest.” Thus, you only need to install the package. Furthermore, we use the package xtables (Dahl et al. (2009)) to convert the R tables to latex tables which we use in the paper.
library("oottest")
library("xtable")Data and predictions can be accessed directly after installing the oottest package. Access them as:
Please see the documentation for each dataset to learn about formatting, usage and the source. To access the documentation for e.g., the data from the two action games, type:
?data_two_action_gamesTable 1 and 2 consist of 6 Vuong matrices, one for each of the different types of games:
The following commands creates a Vuong matrix for each of them and saves them as vuong_table_GAME_NAME. (The ranges below are to select the treatments.)
vuong_table_hdg <- vuong_matrix(data_two_action_games[,1:10], predictions_two_action_games[,1:10,])
vuong_table_mp1 <- vuong_matrix(data_two_action_games[,11:15], predictions_two_action_games[,11:15,])
vuong_table_mp2 <- vuong_matrix(data_two_action_games[,16:20], predictions_two_action_games[,16:20,])
vuong_table_ac <- vuong_matrix(data_three_action_games[,1:10], predictions_three_action_games[,1:10,])
vuong_table_rsp1 <- vuong_matrix(data_three_action_games[,11:15], predictions_three_action_games[,11:15,])
vuong_table_rsp2 <- vuong_matrix(data_three_action_games[,16:20], predictions_three_action_games[,16:20,])Now, we have six Vuong matrix, each looking similar to this:
| CH | CH-RA | LK | NE | NE-RA | NI | NI-RA | QCH | QCH-RA | QLK | QLK-RA | QRE | QRE-RA | RND | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CH | NaN | -1.77 | 3.05 | 7.98 | -1.21 | -0.10 | 1.40 | 0.82 | -1.91 | 1.04 | 2.72 | -0.92 | 0.25 | 3.77 |
| CH-RA | 1.77 | NaN | 5.61 | 6.36 | 0.47 | 2.40 | 5.07 | 3.36 | -1.34 | 2.12 | 5.56 | 1.63 | 3.99 | 7.11 |
| LK | -3.05 | -5.61 | NaN | 4.31 | -3.71 | -6.13 | -5.03 | -6.89 | -5.63 | -1.76 | 1.40 | -4.35 | -6.80 | 6.49 |
| NE | -7.98 | -6.36 | -4.31 | NaN | -5.86 | -6.47 | -4.67 | -5.76 | -6.27 | -9.30 | -2.72 | -7.73 | -5.19 | -3.49 |
| NE-RA | 1.21 | -0.47 | 3.71 | 5.86 | NaN | 1.43 | 3.17 | 2.05 | -1.54 | 1.57 | 5.76 | 1.00 | 2.26 | 4.98 |
| NI | 0.10 | -2.40 | 6.13 | 6.47 | -1.43 | NaN | 2.81 | 4.32 | -2.55 | 0.97 | 2.84 | -1.27 | 0.59 | 6.81 |
| NI-RA | -1.40 | -5.07 | 5.03 | 4.67 | -3.17 | -2.81 | NaN | -2.11 | -5.41 | -0.62 | 2.17 | -2.30 | -8.93 | 12.38 |
| QCH | -0.82 | -3.36 | 6.89 | 5.76 | -2.05 | -4.32 | 2.11 | NaN | -3.46 | 0.07 | 2.50 | -2.34 | -0.81 | 7.62 |
| QCH-RA | 1.91 | 1.34 | 5.63 | 6.27 | 1.54 | 2.55 | 5.41 | 3.46 | NaN | 2.21 | 5.69 | 1.80 | 4.54 | 7.23 |
| QLK | -1.04 | -2.12 | 1.76 | 9.30 | -1.57 | -0.97 | 0.62 | -0.07 | -2.21 | NaN | 2.37 | -2.42 | -0.33 | 2.57 |
| QLK-RA | -2.72 | -5.56 | -1.40 | 2.72 | -5.76 | -2.84 | -2.17 | -2.50 | -5.69 | -2.37 | NaN | -3.01 | -2.92 | -0.74 |
| QRE | 0.92 | -1.63 | 4.35 | 7.73 | -1.00 | 1.27 | 2.30 | 2.34 | -1.80 | 2.42 | 3.01 | NaN | 0.86 | 5.05 |
| QRE-RA | -0.25 | -3.99 | 6.80 | 5.19 | -2.26 | -0.59 | 8.93 | 0.81 | -4.54 | 0.33 | 2.92 | -0.86 | NaN | 11.20 |
| RND | -3.77 | -7.11 | -6.49 | 3.49 | -4.98 | -6.81 | -12.38 | -7.62 | -7.23 | -2.57 | 0.74 | -5.05 | -11.20 | NaN |
In the paper, we colored the matrices to allow for an easier overview. To create the latex used in the paper, one only has to run the function “color_vuong_table” on each table. It outputs latex code which can directly me used as a table in the document.
To create the Vuong matrix using the two and three-action games together, we can not use the vuong_matrix command directly, the structure of two- and three-action games are different.
This is done here. The (hide) output is latex code of a colored Vuong matrix as above.
num_theories <- dim(predictions_two_action_games)[3]
result <- matrix(, nrow = num_theories, ncol = num_theories)
for (i in 1:num_theories) {
for (j in 1:num_theories) {
llr_2 <- oottest:::get_llr(data_two_action_games, predictions_two_action_games[,,i], predictions_two_action_games[,,j])
llr_3 <- oottest:::get_llr(data_three_action_games, predictions_three_action_games[,,i], predictions_three_action_games[,,j])
variance_2 <- oottest:::get_variance_of_llr(data_two_action_games, predictions_two_action_games[,,i], predictions_two_action_games[,,j])
variance_3 <- oottest:::get_variance_of_llr(data_three_action_games, predictions_three_action_games[,,i], predictions_three_action_games[,,j])
result[i, j] <- (llr_2 + llr_3) / (variance_2 + variance_3)^(.5)
}
}
colnames(result) <- colnames(predictions_two_action_games[1,,])
rownames(result) <- colnames(predictions_two_action_games[1,,])
oottest:::color_vuong_table(result)The third and final graph in the paper is a comparison of log-likelihood differences for four different theories.
The graph itself is created in latex using Tikz (Tantau (2013)) which uses the data from R as inputs.
The data was created as follows:
Creating likelihood tables.
llh_table_2 <- oottest:::create_likelihood_table(data_two_action_games, predictions_two_action_games)
llh_table_3 <- oottest:::create_likelihood_table(data_three_action_games, predictions_three_action_games)
llh_table_all <- cbind(llh_table_2,llh_table_3)Output:
| T01 | T02 | T03 | T04 | T05 | T06 | T07 | T08 | T09 | T10 | T11 | T12 | T13 | T14 | T15 | T16 | T17 | T18 | T19 | T20 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CH | -101.89 | -97.48 | -91.01 | -91.01 | -77.43 | -101.89 | -102.01 | -94.90 | -103.95 | -118.19 | -101.89 | -93.60 | -84.55 | -84.55 | -77.43 | -101.89 | -98.71 | -99.40 | -97.46 | -97.60 |
| CH-RA | -101.89 | -97.65 | -93.40 | -91.01 | -77.43 | -94.25 | -109.43 | -96.24 | -101.17 | -99.41 | -101.89 | -93.60 | -84.55 | -84.55 | -77.43 | -101.89 | -98.71 | -99.40 | -97.46 | -97.60 |
| LK | -101.89 | -99.94 | -98.73 | -98.73 | -96.21 | -104.98 | -100.78 | -99.45 | -101.14 | -103.78 | -101.89 | -99.21 | -97.53 | -97.53 | -96.21 | -101.89 | -99.09 | -99.69 | -98.01 | -98.13 |
| NE | -101.89 | -97.73 | -91.73 | -99.23 | -69.27 | -101.89 | -110.40 | -123.37 | -146.11 | -166.82 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -92.87 | -100.52 | -89.57 | -106.11 |
| NE-RA | -101.89 | -98.03 | -92.55 | -90.83 | -70.38 | -101.90 | -110.66 | -97.06 | -101.42 | -99.40 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -95.97 | -96.29 | -86.72 | -86.05 |
| NI | -101.89 | -100.53 | -97.85 | -94.82 | -76.96 | -101.89 | -100.53 | -95.08 | -101.81 | -107.84 | -101.89 | -100.01 | -96.08 | -91.24 | -75.17 | -101.89 | -101.85 | -101.83 | -101.69 | -101.44 |
| NI-RA | -101.89 | -100.80 | -99.02 | -97.42 | -88.86 | -98.96 | -102.75 | -100.64 | -101.79 | -101.15 | -101.89 | -100.35 | -97.72 | -95.26 | -87.92 | -101.89 | -101.82 | -101.79 | -101.61 | -101.43 |
| QCH | -101.89 | -100.80 | -98.64 | -96.11 | -82.15 | -101.89 | -100.75 | -95.85 | -101.14 | -106.19 | -101.89 | -100.39 | -97.25 | -93.33 | -80.91 | -101.89 | -101.86 | -101.85 | -101.74 | -101.58 |
| QCH-RA | -101.89 | -98.01 | -92.92 | -91.32 | -72.85 | -94.57 | -109.52 | -97.02 | -101.40 | -99.40 | -101.89 | -93.74 | -82.24 | -81.27 | -70.25 | -101.89 | -96.58 | -97.56 | -93.41 | -93.68 |
| QLK | -101.89 | -99.02 | -93.73 | -90.67 | -66.42 | -101.89 | -100.16 | -99.10 | -111.82 | -121.28 | -101.89 | -97.75 | -89.70 | -83.40 | -66.79 | -101.89 | -101.53 | -101.32 | -100.14 | -99.14 |
| QLK-RA | -101.89 | -103.76 | -93.73 | -93.65 | -72.68 | -106.42 | -147.95 | -98.76 | -102.55 | -112.66 | -101.89 | -93.61 | -82.47 | -82.41 | -73.46 | -101.89 | -92.88 | -96.83 | -85.68 | -86.48 |
| QRE | -101.89 | -99.50 | -95.28 | -92.19 | -72.14 | -101.89 | -100.10 | -95.11 | -104.33 | -113.18 | -101.89 | -97.96 | -90.24 | -83.63 | -65.59 | -101.89 | -100.98 | -100.52 | -97.58 | -94.63 |
| QRE-RA | -101.89 | -100.18 | -97.52 | -95.53 | -84.32 | -96.90 | -103.56 | -99.89 | -101.72 | -100.66 | -101.89 | -99.08 | -94.42 | -90.76 | -79.92 | -101.89 | -100.45 | -100.03 | -96.87 | -94.60 |
| RND | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 | -101.89 |
| T21 | T22 | T23 | T24 | T25 | T26 | T27 | T28 | T29 | T30 | T31 | T32 | T33 | T34 | T35 | T36 | T37 | T38 | T39 | T40 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CH | -182.37 | -179.56 | -177.11 | -166.42 | -174.78 | -183.77 | -197.40 | -198.12 | -192.14 | -186.98 | -182.37 | -156.82 | -152.52 | -153.38 | -136.17 | -182.37 | -187.23 | -187.63 | -185.82 | -185.22 |
| CH-RA | -204.33 | -179.40 | -177.11 | -166.85 | -172.51 | -152.52 | -169.29 | -167.37 | -168.42 | -152.52 | -182.37 | -156.82 | -152.52 | -153.38 | -136.17 | -182.37 | -187.23 | -187.63 | -185.82 | -185.22 |
| LK | -182.37 | -244.57 | -283.98 | -264.06 | -285.90 | -173.16 | -213.36 | -207.06 | -195.69 | -173.16 | -182.37 | -236.09 | -195.60 | -212.36 | -170.34 | -182.37 | -229.99 | -228.78 | -242.32 | -254.24 |
| NE | -182.37 | -188.15 | -185.69 | -176.20 | -185.60 | -181.44 | -209.76 | -235.91 | -215.17 | -186.47 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -174.00 | -175.08 | -196.50 | -227.22 |
| NE-RA | -183.26 | -183.70 | -179.93 | -174.06 | -176.19 | -143.14 | -168.71 | -171.20 | -167.27 | -140.68 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -176.47 | -174.45 | -178.24 | -186.37 |
| NI | -182.37 | -181.73 | -179.76 | -175.20 | -175.70 | -182.96 | -184.99 | -188.34 | -185.26 | -183.64 | -182.37 | -179.88 | -176.95 | -172.20 | -152.28 | -182.37 | -182.38 | -182.40 | -182.41 | -182.44 |
| NI-RA | -182.48 | -182.20 | -181.10 | -179.24 | -179.34 | -177.08 | -180.28 | -180.86 | -180.28 | -176.61 | -182.37 | -180.35 | -178.52 | -176.27 | -168.13 | -182.37 | -182.40 | -182.42 | -182.43 | -182.45 |
| QCH | -182.37 | -182.08 | -181.20 | -179.23 | -179.21 | -182.59 | -183.29 | -184.40 | -183.30 | -182.83 | -182.37 | -181.40 | -180.22 | -178.17 | -169.25 | -182.37 | -182.37 | -182.37 | -182.38 | -182.38 |
| QCH-RA | -182.41 | -182.29 | -181.83 | -181.08 | -181.09 | -180.25 | -181.53 | -181.77 | -181.54 | -180.07 | -182.37 | -181.59 | -180.86 | -179.93 | -176.60 | -182.37 | -182.37 | -182.38 | -182.38 | -182.38 |
| QLK | -182.37 | -195.47 | -194.83 | -171.94 | -186.71 | -227.55 | -246.48 | -252.28 | -240.16 | -259.68 | -182.37 | -156.11 | -154.25 | -157.96 | -119.50 | -182.37 | -193.60 | -197.52 | -197.48 | -203.35 |
| QLK-RA | -196.37 | -189.94 | -184.78 | -168.04 | -176.90 | -152.69 | -182.03 | -168.60 | -181.41 | -153.03 | -182.37 | -155.13 | -151.29 | -156.93 | -119.49 | -182.37 | -195.69 | -200.08 | -199.45 | -201.30 |
| QRE | -177.81 | -193.79 | -257.43 | -368.06 | -457.30 | -149.34 | -225.60 | -273.00 | -283.93 | -202.21 | -182.37 | -182.30 | -182.58 | -182.51 | -183.17 | -182.37 | -185.30 | -189.30 | -193.90 | -216.65 |
| QRE-RA | -178.11 | -187.08 | -210.73 | -243.32 | -261.23 | -148.06 | -176.48 | -177.83 | -183.69 | -148.48 | -182.37 | -181.95 | -182.12 | -181.62 | -180.89 | -182.37 | -184.48 | -186.54 | -187.21 | -190.50 |
| RND | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 | -182.37 |
Creating a csv file with the log-likelihood difference to the baseline (CH-RA) for each of the four theories: NA-RA,CH-RA (normalized to 1), QLK-RA, QCH-RA
theories <- c("NE-RA", "CH-RA", "QLK-RA", "QCH-RA")
baseline <- llh_table_all["CH-RA", ]
output <- c()
for (theory in theories) {
lh_diff <- round(llh_table_all[theory,] - baseline, 12)
treatment <- 1:40
output <- cbind(treatment, lh_diff)
write.csv(output, file= paste0(theory, ".csv"), row.names = FALSE, quote = FALSE)
}To recreate the tables from the Online Appendix use:
vuong_table_2 <- vuong_matrix(data_two_action_games, predictions_two_action_games)
vuong_table_3 <- vuong_matrix(data_three_action_games, predictions_three_action_games)Creating tables from the log-likelihoods from above (requires xtable):
xtable(llh_table_2, type = "latex")
xtable(llh_table_3, type = "latex")The following code gives us the results of the tests for each theory, if it generates predictions different from the observed data:
chi_sq_hdg <- oottest:::get_all_chi_sq(data_two_action_games[,1:10], predictions_two_action_games[,1:10,])
chi_sq_mp1 <- oottest:::get_all_chi_sq(data_two_action_games[,11:15], predictions_two_action_games[,11:15,])
chi_sq_mp2 <- oottest:::get_all_chi_sq(data_two_action_games[,16:20], predictions_two_action_games[,16:20,])
chi_sq_2 <- oottest:::get_all_chi_sq(data_two_action_games, predictions_two_action_games)
chi_sq_ac <- oottest:::get_all_chi_sq(data_three_action_games[,1:10], predictions_three_action_games[,1:10,])
chi_sq_rsp1 <- oottest:::get_all_chi_sq(data_three_action_games[,11:15], predictions_three_action_games[,11:15,])
chi_sq_rsp2 <- oottest:::get_all_chi_sq(data_three_action_games[,16:20], predictions_three_action_games[,16:20,])
chi_sq_3 <- oottest:::get_all_chi_sq(data_three_action_games, predictions_three_action_games)Here the results for the hawk-dove games:
| chi-sq | p-value | |
|---|---|---|
| CH | 90.65 | 0e+00 |
| CH-RA | 52.48 | 1e-07 |
| LK | 134.97 | 0e+00 |
| NE | 482.47 | 0e+00 |
| NE-RA | 61.20 | 0e+00 |
| NI | 86.14 | 0e+00 |
| NI-RA | 111.10 | 0e+00 |
| QCH | 97.02 | 0e+00 |
| QCH-RA | 47.70 | 7e-07 |
| QLK | 109.56 | 0e+00 |
| QLK-RA | 237.13 | 0e+00 |
| QRE | 81.78 | 0e+00 |
| QRE-RA | 90.01 | 0e+00 |
| RND | 161.05 | 0e+00 |
Now, to create the latex tables as seen in the paper. These can be just copied into the tex document.
table_2 <- cbind(chi_sq_hdg, chi_sq_mp1, chi_sq_mp2, chi_sq_2)
table_3 <- cbind(chi_sq_ac, chi_sq_rsp1, chi_sq_rsp2, chi_sq_3)
xtable(table_2, type = "latex", digits=c(0,2,8,2,8,2,8,2,8))
xtable(table_3, type = "latex", digits=c(0,2,8,2,8,2,8,2,8))Creating tex code of a table of all predictions:
pred_2 <- round(predictions_two_action_games, 3)
th_names <- names(predictions_two_action_games[1,1,])
output <- c()
for (theory in th_names) {
output <- rbind(output, paste0("(", pred_2[1,,theory], ", ", pred_2[2,,theory], ")"))
}
colnames(output) <- names(predictions_two_action_games[1,,1])
rownames(output) <- th_names
xtable(output, type = "latex")
pred_3 <- round(predictions_three_action_games, 3)
output <- c()
for (theory in th_names) {
output <- rbind(output, paste0("(", pred_3[1,,theory], ", ", pred_3[2,,theory], ", ", pred_3[3,,theory], ")"))
}
colnames(output) <- names(predictions_two_action_games[1,,1])
rownames(output) <- th_names
xtable(output, type = "latex")Creating tex code to display the summary of the choice data of the experiments:
xtable(data_two_action_games, type = "latex", digits=0)
xtable(data_three_action_games, type = "latex", digits=0)