*5.1. Model*

Since we wanted to study whether the potential relationship is established and whether the independent variables are constantly changing over time, it was difficult to apply traditional linear and logit models, thus we mainly used the survival model here.

Survival analysis was originally used mainly in biomedical research, focusing on the duration of a particular event, which in this paper refers to the establishment of network relationships. Due to its superiority in addressing temporal variables, this model has since been widely used in other fields such as criminology, economics, sociology, etc. Survival analysis is also widely used in the field of marketing, mostly to analyze consumer decisions and product diffusion [84,85]. One of the more widely used models in survival analysis is the Cox Proportional Hazard Model (Cox PHM) and this paper also focuses on this model form. The model is as follows in Equation (1):

$$h\_i(t, X\_i) \;= h\_0(t) \times \exp(\beta X\_{it}) \tag{1}$$

Here, *hi*(*<sup>t</sup>*, *Xi*) represents the conditional probability that the event of study object *i* does not occur at time *t*−1 but occurs at time *t*. *h*0(*t*) represents the baseline probability that the event occurs at time *t*, similar to the constant term in a linear model. *Xit* represents the vector of covariates affecting the magnitude of the probability of event occurrence, which in this paper mainly refers to user behavior, network structure, and control variables. *β* is the parameter to be estimated corresponding to the covariates. exp(*βXit*) represents the effect of variables on the probability of event occurrence. If the value is greater than 1, it means that the variables will increase the probability of event occurrence. If the value is less than 1, it means that the variables will decrease the probability of event occurrence.
