FYP Analysis
TODO: have joined rounds & exclude NEED TO DEAL WITH CHAT! & FILE LOCATIONS
Pretty pictures
Everything here has bootstrapped 95% CIs.
Should find better curves to fit, but using quadratic to allow for some curvature.
Models
Overall model predicting number of speaker words from block and player count.
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: words ~ block * numPlayers + (block | tangram) + (1 | playerId) + (1 | tangram_group) + (block | gameId)
## Data: model_input (Number of observations: 4013)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~gameId (Number of levels: 60)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 6.19 0.69 5.00 7.74 1.00 2011
## sd(block) 1.55 0.16 1.27 1.91 1.00 1888
## cor(Intercept,block) -0.89 0.04 -0.95 -0.79 1.00 1828
## Tail_ESS
## sd(Intercept) 2276
## sd(block) 2717
## cor(Intercept,block) 2405
##
## ~playerId (Number of levels: 176)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 3.27 0.28 2.76 3.85 1.00 1758 2593
##
## ~tangram (Number of levels: 12)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 5.26 1.25 3.47 8.24 1.00 1591
## sd(block) 0.81 0.20 0.51 1.29 1.00 1825
## cor(Intercept,block) -0.93 0.06 -0.99 -0.76 1.00 2238
## Tail_ESS
## sd(Intercept) 2317
## sd(block) 2445
## cor(Intercept,block) 2297
##
## ~tangram_group (Number of levels: 720)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.99 0.18 2.63 3.33 1.00 1715 2453
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 15.82 3.66 8.69 22.99 1.00 1346 2241
## block -3.22 0.85 -4.95 -1.55 1.00 1544 2375
## numPlayers 1.93 1.07 -0.15 4.02 1.00 1353 1867
## block:numPlayers -0.13 0.26 -0.65 0.40 1.00 1497 2301
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 7.37 0.09 7.19 7.56 1.00 4019 3293
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: words ~ block * numPlayers + block * was_INcorrect + (block | tangram) + (1 | playerId) + (1 | tangram_group) + (block | gameId)
## Data: model_input (Number of observations: 3294)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~gameId (Number of levels: 58)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 5.81 0.67 4.62 7.25 1.00 1799
## sd(block) 1.23 0.15 0.96 1.56 1.00 1598
## cor(Intercept,block) -0.86 0.05 -0.94 -0.75 1.00 2276
## Tail_ESS
## sd(Intercept) 2632
## sd(block) 2672
## cor(Intercept,block) 2601
##
## ~playerId (Number of levels: 172)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.49 0.22 2.09 2.96 1.00 1799 3175
##
## ~tangram (Number of levels: 12)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 4.91 1.20 3.16 7.80 1.00 1917
## sd(block) 0.70 0.19 0.43 1.15 1.00 2227
## cor(Intercept,block) -0.96 0.05 -1.00 -0.85 1.00 2295
## Tail_ESS
## sd(Intercept) 2907
## sd(block) 2890
## cor(Intercept,block) 3339
##
## ~tangram_group (Number of levels: 696)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 3.00 0.16 2.70 3.31 1.00 2194 3171
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 12.99 3.48 6.12 19.86 1.00 1520 2395
## block -2.55 0.72 -3.99 -1.16 1.00 1651 2581
## numPlayers 1.74 1.00 -0.20 3.70 1.00 1715 2536
## was_INcorrect 4.15 0.82 2.54 5.79 1.00 7299 3692
## block:numPlayers -0.06 0.22 -0.47 0.38 1.00 1851 2687
## block:was_INcorrect -0.25 0.30 -0.85 0.33 1.00 7004 3398
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 5.86 0.09 5.70 6.04 1.00 3592 2826
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Pre any listener commentary
What’s the model look like if we discard anything post listener talking? There’s an effect of block, but not a large effect of number of players, no interaction.
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: words ~ block * numPlayers + (block | tangram) + (1 | playerId) + (1 | tangram_group) + (block | gameId)
## Data: model_input (Number of observations: 4001)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~gameId (Number of levels: 60)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 4.97 0.58 3.95 6.21 1.00 1648
## sd(block) 1.31 0.14 1.07 1.62 1.00 1763
## cor(Intercept,block) -0.91 0.04 -0.97 -0.81 1.00 1094
## Tail_ESS
## sd(Intercept) 2295
## sd(block) 2775
## cor(Intercept,block) 1014
##
## ~playerId (Number of levels: 176)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.86 0.23 2.42 3.33 1.00 1168 2214
##
## ~tangram (Number of levels: 12)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 3.78 0.90 2.46 5.98 1.00 1417
## sd(block) 0.53 0.14 0.32 0.89 1.00 1678
## cor(Intercept,block) -0.89 0.10 -0.99 -0.63 1.00 2402
## Tail_ESS
## sd(Intercept) 2208
## sd(block) 1921
## cor(Intercept,block) 2917
##
## ~tangram_group (Number of levels: 720)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.25 0.15 1.96 2.54 1.00 1656 3053
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 15.99 2.95 10.18 21.75 1.00 1271 2035
## block -3.12 0.72 -4.52 -1.74 1.00 1275 1889
## numPlayers 0.65 0.86 -1.05 2.33 1.00 1174 1963
## block:numPlayers 0.11 0.22 -0.32 0.54 1.00 1179 1856
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 6.07 0.08 5.92 6.22 1.00 4371 2666
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).First two rounds only
Speaker’s experience at talking about these images is confounded with player count. However, this isn’t true in the first two rounds, so we can limit to that.
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: words ~ block * numPlayers + (block | tangram) + (1 | playerId)
## Data: model_input (Number of observations: 1413)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~playerId (Number of levels: 118)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 7.70 0.58 6.68 8.94 1.00 1042 1806
##
## ~tangram (Number of levels: 12)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 5.46 1.37 3.40 8.70 1.00 970
## sd(block) 1.00 0.75 0.04 2.75 1.00 1328
## cor(Intercept,block) -0.23 0.49 -0.95 0.84 1.00 3454
## Tail_ESS
## sd(Intercept) 1461
## sd(block) 1789
## cor(Intercept,block) 2256
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 15.91 4.20 7.59 24.10 1.00 685 1301
## block -2.29 4.99 -11.79 7.51 1.00 805 1420
## numPlayers 2.76 1.22 0.27 5.21 1.00 690 1406
## block:numPlayers -1.66 1.60 -4.85 1.38 1.00 792 1359
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 9.81 0.20 9.43 10.21 1.00 4973 2302
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).