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Table 1 Equations to obtain change of intention per week

From: Exploring the emergence and evolution of population patterns of leisure-time physical activity through agent-based modelling

Eq. # Equation Terms
2 \( {p}_{i,t}=\frac{1}{n}\sum \limits_{x=1}^n{b}_{x,t-1}\left[\ln \left(\frac{\alpha_p}{1-{\alpha}_p}\right)\right] \) pi,t is the increment or reduction of person i’s intention in week t due to the behavior of the proximal network, n is the number of people in the proximal network, bx,t-1 is the behavior of person x in the proximal network in week t-1, and αp is the conditional likelihood that people in the proximal network will practice LTPA if it is the best option (i.e., their act reflects the best thing to do)
3 \( {c}_{i,t}=\frac{1}{n}\sum \limits_{x=1}^n{b}_{x,t-1}\left[\ln \left(\frac{\alpha_c}{1-{\alpha}_c}\right)\right] \) ci,t is the increment or reduction of person i’s intention in week t due to the behavior of the perceived community, n is the number of people in perceived community, bx,t-1 is the behavior of person x in the perceived community in week t-1, and αc is the conditional likelihood that people in the perceived community will practice LTPA if it is the best option
4 \( {l}_{i,t}={b}_{i,t-1}\left[\ln \left(\frac{\alpha_b}{1-{\alpha}_b}\right)\right] \) li,t is the increment or reduction of person i’s intention in week t due to his previous behavior, bi,t-1 is the behavior of person i in week t-1, and αb is the conditional probability that a person will practice LTPA if it is the best option
5 \( {w}_{i,t}=1-\frac{\left|{i}_{i,t-1}\right|}{\ln \left(\frac{0.97}{0.03}\right)} \) wi,t represents the intention strength of person i in week t, ii,t-1 is the person i’s intention in week t-1
6 \( {y}_{h,i}=\left[\ln \left(\frac{u_{h,i}}{1-{u}_{h,i}}\right)\right]\frac{1}{r} \) yh,i is the log-odds of the highest perceived utility (uh,i), r is a scaling factor (set by the modeler, 100 in this work) to re-scale the magnitude of the built environment’s influence
7 \( {i}_{i,t}={i}_{i,t-1}+{w}_{i,t}\left({p}_{i,t}+{c}_{i,t}+{l}_{i,t}+{y}_{h,i}\right) \) ii,t is the level of intention of person i in week t
  1. LTPA Leisure-time physical activity