Threshold Regression And The Application Of Improved Operational Time Scale Threshold Regression On Marketing Data

The popularization of the Internet has promoted the booming development of e-commerce.,and online marketing is one of the most important section of e-commerce.Currently,marketing data are commonly modeled and analyzed by Logistic regression,which is simple and easy to understand.Survival analysis models on the other hand,not only have their own advantage on the usage of time information,but also perform well on modeling the censored data,comparing with the Logistic models.Threshold regression,as one type of survival analysis models,has received more and more attention in recent years.Compared with the most common model Cox proportional hazard model in survival analysis,the threshold regression does not need to assume that independent variables must satisfy proportional hazard assumption,and its assumption on potential stochastic process is close to reality,and the model result has stronger interpretability.These advantages bring threshold regression to huge potential in marketing data modeling.This paper gives a simple introduction to threshold regression and operational time scale threshold regression model.Based on the operational time scale threshold regression model,we linked the covariates to the coefficients of different states of calendar time,so that individuals will have different conversion rates with the same state of time and have a stronger ability to model and interpret individual differences.In the simulation study,we generated 200 and 1000 survival data samples respectively.The results show that the estimation of the real parameters by running time-scale regression considering individual differences is unbiased.In the chapter of empirical research,we extract a survival data of 2144 observations and 14 features by cleaning a log from mobile consumers of Taobao.The backward elimination stepwise regression method using BIC as the evaluation criterion selects the optimal combination of variables for Logistic regression including survival time information,Logistic regression excluding survival time information,and classical threshold regression in the training samples from the data above.The results of the three models in the test set showed that,compared with the Logistic regression,the threshold regression has a higher recall rate and F1 metric,so the threshold regression model has more important practical significance under this context.The empirical research results of the improved operational time scale threshold regression verify many intuitive business knowledge: such as consumers with browsing behavior and shopping cart behavior have a stronger purchasing tendency;but the model also provides some new perspectives,for example,consumers with excessive views will reduce the probability of purchases,and the behavior of adding goods to favorites list will not help the conversion of purchases.At the end of the paper,the future development direction of the model is proposed as follows: random effects model.By introducing a random effect model,the model will enhance its fitting ability on individual differences caused by unobserved variables.