Effect of estimation method, definition of ratio, and the plausible range in estimating social network size

A prime for network scale-up studies is the calculation of network size (C). To estimate C, respondents are asked about the number of their acquaintances belonging to specific reference groups with known sizes. The aim of this manuscript is to address influence of method of estimation and exclusion of unreliable reference groups on C. Recruiting 1275 women and using 25 reference groups, C was calculated applying traditional and Means of Sums (MoS) estimators. This C is applied to back-calculate the size of reference groups. To assess the closeness of back-calculated and real size, two types of ratio were calculated: back-calculated over real size, and its reverse. The tolerable range for ratio was defined as (0.5, 1.5), (0.5, 2), and < 1 based on the absolute logarithmic scale. The reference group corresponding to the poorest ratio was omitted. New C was estimated based on the remainder of the reference groups. The whole process continued in an iterative fashion until all ratios fall within the plausible range. In the traditional approach, C was robust with respect to definition of ratio and its tolerable range. Minimum and maximum C were 174 and 186. In the MoS analysis, C values hugely diverse ranged 185–557. This might partially be due to small number of eligible reference groups contributing in the estimation of C. As C is used to estimate size of hidden groups, its calculation needs careful plan. We recommend authors to provide a range of values for C.