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Table 5 Comparison of the normalised root mean squared error (NRMSE) [see Eq. (12)] between the models of attention

From: Public risk perception and emotion on Twitter during the Covid-19 pandemic

NRMSE country Power law Weber–Fechner law Linear relationship
Argentina 0.114 0.113 0.116
Australia 0.173 0.171 0.175
Canada 0.106 0.105 0.117
Chile 0.151 0.149 0.17
Colombia 0.143 0.144 0.145
India 0.126 0.128 0.125
Mexico 0.1 0.101 0.133
Nigeria 0.223 0.222 0.218
South Africa 0.184 0.183 0.188
Spain 0.202 0.198 0.193
UK 0.149 0.143 0.166
USA 0.139 0.126 0.179
Mean 0.151 0.149 0.16
Proportion of best fits 16.7% 58.3% 25%
Proportion of second-best fits 66.7% 33.3% 0 %
  1. We compare the power law model of Eq. (11), the Weber–Fechner model of Eq. (10), and a linear relationship between variables, which we use as a benchmark model. Lower values indicate better-fitting models; italics indicate the best model for that country. Note that, overall, the Weber–Fechner law outperforms the other models. For further details, see Figs. 8 and 9 in “Appendix 1”