Figure 1.

Models of contact reporting probabilities. (a) Contact reporting probabilities based on pairs of survey reports (^ss), where a circle stands for a contact reported (grey) or not reported (white) by a survey participant. There are four possible combinations: (i) ${\mathit{N}}_1^{\mathit{ss}}$ where both contact partners report the contact, (ii) ${\mathit{N}}_2^{\mathit{ss}}$ and (iii) ${\mathit{N}}_3^{\mathit{ss}}$ where only one of the contact partners report the contact (since ${\mathit{N}}_2^{\mathit{ss}}$ and ${\mathit{N}}_3^{\mathit{ss}}$ are indistinguishable, we use their sum ${\mathit{N}}_{2+3}^{\mathit{ss}}$), and (iv) ${\mathit{N}}_4^{\mathit{ss}}$ where none of the two contact partners report the contact. (b) All possible combinations of survey reporting statuses, where P stands for the probability of reporting a contact and Q is the complement. (c) Survey reports and mote detections of contacts combined (^sm), where a rectangle stands for a contact detected (grey) or not detected (white) by a pair of motes. There are four possible combinations: (i) ${\mathit{N}}_1^{\mathit{sm}}$ where a contact pair is reported in the survey and recorded by motes, (ii) ${\mathit{N}}_2^{\mathit{sm}}$ and (iii) ${\mathit{N}}_3^{\mathit{sm}}$ where only the survey or motes recorded the contact, and (iv) ${\mathit{N}}_4^{\mathit{sm}}$ where a contact that actually took place was neither reported nor detected by a mote. (d)P_s and P_m stand for average survey and mote reporting probabilities, and Q_s and Q_m are the average probability of a survey or mote not recording a contact respectively. (e) The estimated proportion of the difference between survey and mote data that can be attributed to survey underreporting, based on the models (b) and (d). Here, ${\mathit{N}}_{1\text{'}}^{\mathit{sm}}$ is the estimated amount of contacts detected by the motes and also reported by the study participants if there was no underreporting (estimate is based on P), ${\mathit{N}}_{1\text{'}}^{\mathit{sm}}-{\mathit{N}}_1^{\mathit{sm}}$ is the estimated amount of mote-detected but not survey-reported contacts due to underreporting, and ${\mathit{N}}_{3\text{'}}^{\mathit{sm}}$, is the estimated amount of non-reporting due to differences in contact definitions between the survey and mote studies.