New prediction method for the mixed logistic model applied in a marketing problem

When units belong to a specific group, such as employees nested within companies, the data present a hierarchical structure that can be modeled by using mixed models. In addition to fixed effects, these models estimate the random effects for each group. The problem of assigning values to the random effects for new groups in order to predict the outcome in a future period, based on the parameters previously estimated, is the focus of this article. The empirical best predictor (EBP) has been applied to the logistic mixed model, but when there is more than one random effect, the processing time required to solve the multidimensional integrals is costly. A new methodology is proposed based on linear regression that considers the relationship among the random effects and the covariates aggregated at the group level. A comparison among the linear regression prediction method (LRPM), EBP, and the ordinary logistic model is provided through simulation studies and an application study with a mobile company. The results indicate that LRPM drastically reduced the computational effort, and at the same time, maintained a similar level of prediction in relation to EBP.