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Table 3 Estimate of repeatability for unstructured competition

From: Validation of models for analysis of ranks in horse breeding evaluation

Simulations
Number of horses 1000 1000 1000 1000 1000 1000
Number of events 2500 1000 500 400+400+200 10000 2500
Number of events per horse 10 10 10 10 40 10
Number of horses per event 4 10 20 5/10/20 4 4
Total number of ranks 10000 10000 10000 10000 40000 10000
Simulated repeatability 0.25 0.25 0.25 0.25 0.25 0.10
Repeatability estimated
True underlying performance 0.251 0.249 0.251 0.249 0.251 0.100
Ranks and Underlying model 0.251 0.252 0.253 0.248 0.253 0.099
Normal Score 0.145 0.199 0.222 0.196 0.144 0.057
Raw ranks 0.144 0.197 0.218 0.068 0.144 0.057
Standard deviation of repeatability over replicate
True underlying performance 0.009 0.012 0.012 0.011 0.007 0.007
Ranks and Underlying model 0.010 0.015 0.012 0.011 0.007 0.007
Normal Score 0.007 0.012 0.011 0.008 0.004 0.004
Raw ranks 0.007 0.012 0.011 0.005 0.004 0.004
Regression coefficient between simulated and estimated competing ability
True underlying performance 0.997 1.006 1.004 0.992 1.003 1.014
Ranks and Underlying model 0.998 0.997 1.004 0.996 1.004 1.013
Normal Score 1.406 1.160 1.088 1.157 1.413 1.374
Raw ranks 1.408 1.169 1.101 2.696 1.414 1.374
  1. 20 replicates of each simulated scenario