Table 2 Posterior mean β-coefficients and 95% posterior intervals for the Bayesian logistic generalized linear models using choice of the option with the higher EV as the dependent variable.

	TEM	DEM Attention allocation	DEM α	DEM θ	DEM α, θ	DEM α, θ, attention allocation
All data	loo−IC = 8336.3	loo−IC = 8031.3	loo−IC = 7913.5	loo−IC = 8233.9	loo−IC = 7848.9	loo−IC = 7525.2
Intercept	0.945 [0.894; 0.996]	0.993 [0.937; 1.048]	1.025 [0.97; 1.079]	0.963 [0.91; 1.014]	1.039 [0.983; 1.094]	1.089 [1.029; 1.147]
Numeracy	0.176 [0.124; 0.227]	0.188 [0.134; 0.243]	0.094 [0.038; 0.148]	0.112 [0.057; 0.166]	0.045 [− 0.013; 0.103]	0.06 [0.002; 0.115]
Attention allocation		0.481 [0.429; 0.536]				0.511 [0.453; 0.57]
α			0.611 [0.551; 0.673]		0.596 [0.533; 0.657]	0.633 [0.569; 0.696]
θ				0.285 [0.23; 0.341]	0.234 [0.178; 0.289]	0.234 [0.176; 0.294]

Risky.better data	loo−IC = 4695.9	loo−IC = 4120.7	loo−IC = 4549.9	loo−IC = 4658	loo−IC = 4532.1	loo−IC = 4026.6
Intercept	− 0.094 [− 0.161; − 0.026]	− 0.147 [− 0.223; − 0.073]	− 0.09 [− 0.159; − 0.019]	− 0.094 [− 0.16; − 0.027]	− 0.088 [− 0.16; − 0.019]	− 0.145 [− 0.22; − 0.071]
Numeracy	0.268 [0.199; 0.34]	0.235 [0.163; 0.309]	0.193 [0.123; 0.264]	0.175 [0.101; 0.248]	0.131 [0.055; 0.207]	0.118 [0.036; 0.2]
Attention allocation		0.988 [0.897; 1.081]				0.955 [0.858; 1.048]
α			0.449 [0.375; 0.524]		0.426 [0.349; 0.503]	0.345 [0.263; 0.43]
θ				0.238 [0.165; 0.313]	0.176 [0.096; 0.254]	0.172 [0.091; 0.258]

Safe.better data	loo−IC = 1467.5	loo−IC = 1350.5	loo−IC = 1465.6	loo−IC = 1380.6	loo−IC = 1381.7	loo−IC = 1258.1
Intercept	2.924 [2.785; 3.074]	3.267 [3.074; 3.455]	2.935 [2.788; 3.085]	3.145 [2.973; 3.323]	3.152 [2.977; 3.327]	3.523 [3.308; 3.751]
Numeracy	0.12 [− 0.024; 0.263]	0.198 [0.052; 0.34]	0.096 [− 0.055; 0.245]	0.046 [− 0.115; 0.202]	0.039 [− 0.12; 0.198]	0.11 [− 0.062; 0.274]
Attention allocation		0.954 [0.773; 1.135]				1.015 [0.827; 1.216]
α			0.149 [− 0.005; 0.31]		0.05 [− 0.111; 0.219]	0.13 [− 0.045; 0.315]
θ				0.701 [0.552; 0.853]	0.697 [0.541; 0.845]	0.711 [0.555; 0.868]

Results are shown separately for analyses across all data (top panel), analyses including only data from risky.better problems (middle panel), and analyses including only data from safe.better problems (bottom panel). The TEMs and DEMs included different combinations of predictor variables (numeracy, attention allocation, α, and/or θ). Continuous predictor variables were z-standardized. Coefficients and 95% Posterior Intervals are reported for all predictors included in a given model. Loo—IC indicates the leave-one-out information criterion. Lower values of loo—IC indicate a better predictive performance of the model compared to other models estimated using the same data. Boldface indicates credible effects. TEM = Total Effect Model. DEM = Direct Effect Model.

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